{"id":1366,"date":"2023-03-22T17:06:10","date_gmt":"2023-03-22T17:06:10","guid":{"rendered":"https:\/\/vartmaaninstitutesirsa.com\/?page_id=1366"},"modified":"2024-03-05T05:47:02","modified_gmt":"2024-03-05T05:47:02","slug":"chapter-7-motion","status":"publish","type":"page","link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/chapter-7-motion\/","title":{"rendered":"Chapter 7 Motion"},"content":{"rendered":"\r\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Chapter 7 Motion<\/h1>\r\n\r\n\r\n\r\n

Motion:\u00a0 Distance and displacement, velocity; uniform and non-uniform motion along a straight line; acceleration, distance-time and velocity-time graphs for uniform motion and uniformly accelerated motion, elementary idea of uniform circular motion.<\/p>\r\n

To read\/ download class notes of chapter 7 motion click on the link given in the end of the chapter.<\/span><\/h4>\r\n
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\"C:\\Users\\dell\\Desktop\\VATMAAN\u00a0 \u00a0 \u00a0<\/em><\/strong>SANDEEP SONI\u2019S PHYSICS<\/span><\/strong>\u00a0<\/span><\/strong>COMPETITION CLASSES<\/span><\/strong>\u00a0\u00a0<\/sub><\/span><\/strong><\/p>\r\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><\/strong>(10+1, 10+2, IIT-JEE<\/span><\/strong>\u00a0(<\/span>Main & Advance<\/span>),<\/span>\u00a0NEET, B.Sc.\u00a0<\/span><\/strong>Agriculture<\/span>,\u00a0<\/span>NDA)\u00a0<\/span><\/strong><\/p>\r\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/strong>OPP: JHUNTHARA DHARAMSHALA\u00a0<\/span>NEAR SURKHAB<\/span>\u00a0CHOWK,\u00a0<\/span>HISSAR ROAD SIRSA<\/span>\u00a0<\/span><\/p>\r\n

\"\"<\/span>\"\"<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/u><\/p>\r\n<\/div>\r\n

In daily life we observe that some substances are in rest & some are in motion. Study of Motion of objects is very important in physics.<\/span><\/p>\r\n

    \r\n
  1. Mechanics:-<\/span><\/u><\/li>\r\n<\/ol>\r\n

    Mechanics is that branch of physics which deals with the motion of objects and the equilibrium of the object under many forces<\/span><\/em>.<\/span><\/p>\r\n

      \r\n
    • Statics:-<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

      It deals with the objects which are at rest or we can say that it deals with the object which is under equilibrium under many force<\/span><\/em><\/p>\r\n

        \r\n
      • Kinematics:-<\/span><\/u><\/strong>\u00a0<\/span><\/li>\r\n<\/ul>\r\n

        It deals with the motion of object without considering the cause of motion<\/span><\/em>.<\/span><\/p>\r\n

          \r\n
        • Dynamics:-<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

          \u00a0<\/span>It deals with the motion of object along with the cause of motion of object.<\/span><\/em><\/p>\r\n

          2. REST AND MOTION:-<\/span><\/u><\/strong><\/p>\r\n

            \r\n
          • REST:-<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

            If an object does not change its position of rest with respect to surrounding than it is called in rest.<\/span><\/em>\u00a0<\/span><\/p>\r\n

            E.g.:- a book placed on the table.<\/span><\/p>\r\n

              \r\n
            • Motion:-<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

              If an object changes its position w.r.t to surrounding than it is called in motion.\u00a0<\/span><\/em><\/p>\r\n

              E g,<\/span>\u00a0\u00a0<\/span>A moving car on the road etc.<\/span><\/p>\r\n

                \r\n
              • Rest & motion are relative terms explain\u00a0<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

                Sometimes we see that objects are in rest but actually they are in motion like a person sitting<\/span>\u00a0\u00a0<\/span>in train see that another persons are in rest but they are in motion.<\/span><\/p>\r\n

                \u00a0<\/span>Similarly sometimes we see that objects are in motion but they found in rest, like a person in vehicle see that trees are moving but actually they are in rest.<\/span><\/p>\r\n

                \u00a0<\/span>Hence we cannot say that a object is in rest or in motion. These are relative term.\u00a0<\/span><\/p>\r\n

                3. Motion in one, two & three dimensions:-<\/span><\/u><\/strong><\/p>\r\n

                  \r\n
                • ONE DIMENSION MOTION:\u00a0<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

                  A particle moving along a straight line or path is said to be posses\u2019 one dimensional motion<\/span><\/em>. I,e only one co- ordinate axis changes w.r.t time. E.g- Motion of train on straight track, motion of bus on straight road etc.\u00a0<\/span><\/p>\r\n

                    \r\n
                  • TWO DIMENSIONAL MOTIONS:-\u00a0<\/span><\/u><\/strong><\/li>\r\n<\/ul>\r\n

                    A particle moving in a plane is said to be passes two dimensional motion I.e. only two co-ordinate axis changes w.r.t time<\/span><\/em>. e.g. – Motion of insect on the floor, motion of earth around the sun.<\/span><\/p>\r\n

                      \r\n
                    • THREE DIMENSIONAL MOTIONS:-<\/span><\/u><\/strong>\u00a0<\/span><\/li>\r\n<\/ul>\r\n

                      A particle moving in space is said to be passes three dimensional motion<\/span><\/em>\u00a0I.e. all the three co- ordinate axis changes with respect to time e.g- A bird, an aero plane flying in the sky etc.<\/span><\/p>\r\n

                      4. Frame of reference:-<\/span><\/u><\/strong><\/p>\r\n

                      \"FrameThe fixed point or place with respect to which the position, velocity or acceleration of an object is measured is called frame of reference.<\/span><\/em><\/p>\r\n

                      Cartesian co-ordinate system:-<\/span><\/u><\/strong><\/p>\r\n

                      Draw two mutually perpendicular line OX & OY<\/span>\u00a0<\/span><\/strong>meeting at a point O. Here O is called origin &<\/span>\u00a0<\/span><\/strong>OX & OY called co-ordinate axis. And the region<\/span>\u00a0<\/span><\/u><\/strong>covered by OX & OY is a plane. This system is<\/span>\u00a0<\/span><\/u><\/strong>called Cartesian co-ordinate system.\u00a0<\/span><\/p>\r\n

                      5. TYPES OF MOTION:-<\/span><\/u><\/strong><\/p>\r\n

                      A body can have three type of motion:-<\/span><\/p>\r\n

                      \u00a0<\/span><\/strong>(i)-\u00a0<\/span><\/strong>Translational motion:-<\/span><\/u><\/strong>\u00a0<\/span><\/strong><\/p>\r\n

                      \u00a0<\/span><\/em><\/strong>If line joining the two points remains parallel to itself throughout the motion is called translational motion. e.g.<\/span><\/em>\u00a0\u00a0<\/span><\/em>A bus moving on straight road.<\/span><\/em><\/p>\r\n

                      (ii<\/span><\/strong>)- Rational motion:-<\/span><\/u><\/strong>\u00a0<\/span><\/strong><\/p>\r\n

                      \u00a0<\/span><\/strong>If a body moving around a fixed axis is called rotational motion. E.g.<\/span><\/em>\u00a0\u00a0<\/span><\/em>Motion of earth around sun etc.<\/span><\/em><\/p>\r\n

                      (iii<\/span><\/strong>)-\u00a0<\/span><\/u><\/em><\/strong>Vibration motion:-<\/span><\/u><\/strong>\u00a0<\/span><\/p>\r\n

                      If a body moves to & fro about a mean position after a regular interval of time is called Vibration motion<\/span><\/em>. E.g.- Motion of pendulum.<\/span>\u00a0Scalar and Vectors<\/span><\/u><\/strong><\/p>\r\n

                      6.PHYSICAL QUANTITY<\/span><\/u><\/strong><\/p>\r\n

                      In the study of the two dimensional motion of the physical quantity we need sometime both magnitude and the direction of the quantity so introduced a new term vector.<\/span><\/em><\/p>\r\n

                      A physical quantity may be divided into two types\u00a0<\/span><\/p>\r\n

                      Scalar Quantity:-<\/span><\/u><\/strong><\/p>\r\n

                      Physical quantities that have only magnitude and no direction are called scalar quantities or scalars. Eg: mass, time, speed etc.<\/span><\/p>\r\n

                      Vector Quantity:-<\/span><\/u><\/strong><\/p>\r\n

                      Physical quantities that have both magnitude and direction are called vector quantities or vectors. Eg: displacement, weight, velocity, force etc.<\/span><\/p>\r\n

                      Difference between scalar and vector quantity<\/span><\/em><\/strong><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                      \r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/em>Scalar quantity<\/span><\/em><\/p>\r\n<\/td>\r\n

                      		\r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/em>Vector quantity<\/span><\/em><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      1.Scalar quantity have only magnitudes<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      1.Vector quantity have both magnitude and direction<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      2.Scalar quantity changes when magnitude of the quantity changes\u00a0<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      2.Vector quantity changes when either magnitude or direction changes<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      3.Scalar can be added by the ordinary laws of the algebra<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      3.Vectors can be added by only special laws of<\/span>\u00a0\u00a0<\/span>vector<\/span>\u00a0\u00a0<\/span>addition<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

                      16\u00a0<\/span>Representation of vectors<\/span><\/strong>\u00a0<\/span><\/p>\r\n

                      A vector is represented by using a straight line with an arrowhead at one end. The length of the line represents the magnitude of the vector and the arrowhead gives its direction.<\/span><\/p>\r\n

                      \"Representation<\/p>\r\n

                      \u00a0<\/span><\/p>\r\n

                      \u00a0<\/span><\/p>\r\n

                       <\/p>\r\n

                      7. DISTANCE AND DISPLACEMENT:-<\/span><\/u><\/strong><\/p>\r\n

                      \u00a0<\/span><\/u><\/strong>DISTANCE:-<\/span><\/u><\/strong><\/p>\r\n

                      The length or actual path followed by an object between two points in a given interval of time is called distance.<\/span><\/em><\/p>\r\n

                      DISPLACEMENT:-<\/span><\/u><\/strong><\/p>\r\n

                      The straight line path between any two objects is called displacement.<\/span><\/em><\/p>\r\n

                      *Give any five differences between distance and displacement\u00a0<\/span><\/strong><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                      \r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Distance<\/span><\/u><\/strong>\u00a0<\/span><\/u><\/strong>\u00a0\u00a0\u00a0\u00a0<\/span><\/u><\/strong>\u00a0\u00a0\u00a0\u00a0<\/span><\/u><\/strong>\u00a0\u00a0\u00a0\u00a0<\/span><\/u><\/strong><\/p>\r\n<\/td>\r\n

                      		\r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Displacement<\/span><\/u><\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      1 Distance is actual path followed by an object between two points.<\/span>\u00a0<\/span>\u00a0<\/span>\u00a0<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      1 Displacement is the straight line distance followed by the object.\u00a0<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      2<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>It is a scalar quantity<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      2<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>It is a vector quantity.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      3<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>It is always +ve<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      3<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>It may be +ve, -ve or zero.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      4<\/span>\u00a0\u00a0<\/span>Distance may be equal to or Greater than displacement<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      4<\/span>\u00a0\u00a0<\/span>Displacement may be equal to or smaller than distance<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                      \r\n

                      5<\/span>\u00a0\u00a0\u00a0<\/span>Distance per unit time is speed.<\/span><\/p>\r\n<\/td>\r\n

                      		\r\n

                      5 Displacement per unit time is velocity.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

                      QUESTION 1: A person moves on a semi-circular track of radius 40.0 m during a morning walk. If he starts at one end of the track and reaches at the other end, find the distance covered and the displacement of the person.\u00a0<\/span><\/strong><\/p>\r\n

                      Solution :<\/span>\u00a0\u00a0<\/span>The distance covered by the person equals the length of the track.<\/span><\/p>\r\n

                      It is equal to\u00a0<\/span>\"\"<\/p>\r\n

                      The displacement is equal to the diameter of the semi-circular track joining the two ends. It is\u00a0<\/span>\"\"\u00a0<\/span><\/p>\r\n

                      \"\"QUESTION\u00a0<\/span><\/strong>2: Find the distance and displacement of a particle travelling from one point to another, say from pt. A to B, in a given path.\u00a0<\/strong><\/p>\r\n

                      Sol: Total distance travelled = 10+50+40+55+ (40 – 10) = 185 m<\/p>\r\n

                      Total Displacement = 50 + 55 =105 m<\/p>\r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/strong><\/p>\r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/strong>\u00a0<\/span><\/u><\/strong>8. SPEED AND VELOCITY:-<\/span><\/u><\/strong><\/p>\r\n

                      (a) Speed:-<\/span><\/u><\/strong><\/p>\r\n

                      The distance travelled by the body per unit time is called speed<\/span><\/em>.<\/span><\/p>\r\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Speed=\u00a0<\/span>\"\"<\/p>\r\n

                      Unit of speed:- m\/s in\u00a0<\/span>S.I,<\/span><\/strong>\u00a0in c,g,s system cm\/sec.<\/span>\u00a0\u00a0<\/span><\/p>\r\n

                      *speed is a scalar quantity. It may be +ve or zero<\/span><\/p>\r\n

                      Types of speed<\/span><\/u><\/strong><\/p>\r\n

                        \r\n
                      1. Uniform Speed:-<\/u> \u00a0<\/span><\/li>\r\n<\/ol>\r\n

                        A particle or body is said to be moving with uniform speed if it cover equal distance in equal interval of time. Sometime it is called constant speed.<\/span><\/em><\/p>\r\n

                        \u00a0<\/span><\/strong><\/p>\r\n

                          \r\n
                        1. Variable velocity<\/u>:-<\/li>\r\n<\/ol>\r\n

                          Particle or body is said to be moving with variable speed if it cover unequal<\/span><\/em>\u00a0<\/span><\/em><\/strong>distance in equal interval of time or equal distance in unequal interval of time.<\/span><\/em><\/p>\r\n

                            \r\n
                          1. Average speed:-<\/u><\/li>\r\n<\/ol>\r\n

                            Average speed of a body is defined as the ratio of<\/span><\/em>\u00a0<\/span><\/em><\/strong>total distance travelled by the body to the total time taken<\/span><\/em>.<\/span><\/p>\r\n

                            V<\/span>av<\/sub><\/span>\u00a0=\u00a0<\/span>\"\"<\/p>\r\n

                            *It may be noted that particle may or may not have speed equal to average speed at any instant.<\/span><\/p>\r\n

                            *Speed is equal to average speed only when particle moves with uniform speed.<\/span><\/p>\r\n

                            QUESTION 3:<\/span><\/strong>\u00a0A man walks at a speed of 6 km\/hr for 1 km and 8 km\/hr for the next 1 km. What is his average speed for the walk of 2 km ?\u00a0<\/strong><\/p>\r\n

                            Solution :\u00a0 Distance travelled is 2 km.\u00a0\u00a0<\/p>\r\n

                            Time taken \"\"<\/p>\r\n

                            Average speed \"\".\u00a0<\/u><\/p>\r\n

                              \r\n
                            1. Instantaneous speed:-<\/u><\/li>\r\n<\/ol>\r\n

                              The speed of an object at any instant of time is called instantaneous speed<\/span><\/em>\u00a0\u00a0\u00a0<\/span><\/em>To calculate Instantaneous we have to make \u2206x as small as possible so that the speed of the body does not change during interval. <\/span><\/p>\r\n

                              Hence<\/span>\u00a0\u00a0\u00a0<\/span>V<\/span>ins<\/sub><\/span>\u00a0= Lim<\/span>\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\r\n

                              (B) Velocity:-<\/span><\/u><\/strong>\u00a0<\/span><\/p>\r\n

                              The displacement of a particle or body per unit time is called velocity of the body<\/span><\/em>.<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>.<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\r\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\r\n

                              Velocity is a vector quantity. It can be +ve, -ve & zero.<\/span><\/p>\r\n

                              Types of velocity:-<\/span><\/u><\/strong><\/p>\r\n

                              (1)- Uniform velocity (ii) variable velocity (iii) Average velocity (iv) Instantaneous Velocity.<\/span><\/p>\r\n

                              * All these velocities can be defined by types of speed by only replacing speed by velocity & distance by displacement.<\/span><\/p>\r\n

                              9. Difference between speed & velocity<\/span><\/u><\/strong><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                              \r\n

                              S<\/span><\/strong>peed<\/span><\/u><\/em><\/strong><\/p>\r\n<\/td>\r\n

                              		\r\n

                              V<\/span><\/strong>elocity<\/span><\/u><\/em><\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                              \r\n

                              It is the ratio of distance to the time.<\/span><\/p>\r\n<\/td>\r\n

                              		\r\n

                              It is the ratio of displacement to the time.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                              \r\n

                              It is a scalar quantity.<\/span><\/p>\r\n<\/td>\r\n

                              		\r\n

                              It is a vector quantity.\u00a0<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                              \r\n

                              It may be +ve or zero.<\/span><\/p>\r\n<\/td>\r\n

                              		\r\n

                              It may be +ve,-ve or zero<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                              \r\n

                              It has only magnitude.<\/span><\/p>\r\n<\/td>\r\n

                              		\r\n

                              It has both magnitude & direction.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

                              \r\n

                              Speed may be equal to or greater than velocity.<\/span><\/p>\r\n<\/td>\r\n

                              		\r\n

                              Velocity may be equal to or smaller than speed<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

                              QUESTION\u00a0<\/span><\/strong>4: If a train moves from station A to B with a constant speed v =40 km\/h and returns back to the initial point A with a constant speed V2=30 km\/h, then calculate the average speed and average velocity.<\/strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n

                              Sol: Average speed is distance covered divided by time taken. Distance is length of the path travelled. Average velocity is displacement divided by time taken. Displacement is the vector from initial point to final point.<\/p>\r\n

                              Let the distance AB = s, Time taken by train from A to B\"\"<\/p>\r\n

                              Time taken by train From B to A,<\/p>\r\n

                              \"\"<\/p>\r\n

                              \"If<\/p>\r\n

                              \"\"\u00a0<\/p>\r\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \"\"<\/p>\r\n

                              \"Consider\u00a0QUESTION 7:<\/span><\/strong>\u00a0\u00a0<\/strong>Consider a train moving from station A to B with a constant speed of 40 km\/h for half the time and<\/strong>\u00a0\u00a0<\/strong>with constant speed of 30 km\/h for the next half time of that journey. Calculate the average speed of the whole journey.\u00a0<\/strong><\/p>\r\n

                              Sol:\u00a0 Let AB = s and T = Total time of journey.<\/p>\r\n

                              Distance travelled in first half time\"\"\u00a0is, \"\"\u00a0 .<\/p>\r\n

                              Distance travelled in second half time is,\"\"<\/p>\r\n

                              Or\u00a0 \u00a0\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\r\n

                              Or\u00a0 \u00a0 \u00a0 \u00a0 \"\"<\/p>\r\n

                              \u00a0<\/span><\/strong><\/p>\r\n

                              10. DISPLACEMENT TIME GRAPH<\/span><\/u><\/strong><\/p>\r\n

                              \"DISPLACEMENTFor uniform motion displacement time graph or position time graph is a straight line making an angle O with X axis.<\/span><\/p>\r\n

                              Determination of velocity from position-time graph<\/span><\/u><\/strong><\/p>\r\n

                              Consider two points A & B on the straight line the position<\/span>\u00a0\u00a0<\/span>& time corresponding to A & B are (T<\/span>1<\/sub><\/span>, X<\/span>1<\/sub><\/span>) & (T<\/span>2,<\/sub><\/span>x<\/span>2<\/sub><\/span>) respectively.<\/span><\/p>\r\n

                              Now the displacement of the body co-responding to time interval (T<\/span>2<\/sub><\/span>-T<\/span>1<\/sub><\/span>) is (X<\/span>2<\/sub><\/span>-X<\/span>1<\/sub><\/span>)<\/span><\/p>\r\n

                              So,\u00a0<\/span>\u00a0<\/span>Velocity of the body=<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\r\n

                              OR<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\"\"\u03b8<\/span>\u00a0<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\r\n

                              \"\"\u00a0\u00a0<\/span>Represents the slop of the line<\/span><\/p>\r\n

                              \"Two\u00a0Hence we can say that velocity of a body having uniform motion = Slope of the displacement<\/span>\u00a0<\/span><\/strong>time graph<\/span><\/p>\r\n

                              \u00a0<\/span><\/strong><\/p>\r\n

                              \u00a0<\/span><\/strong><\/p>\r\n

                              QUESTION 8:<\/span><\/strong>\u00a0<\/strong>Two bodies having their displacement time graph as shown in fig. which one have larger velocity<\/span><\/strong>.<\/span><\/p>\r\n

                              Ans:- Slope of B is greater so B have larger velocity.<\/span><\/p>\r\n

                              \u00a0<\/span><\/strong><\/p>\r\n

                              11. VELOCITY-TIME GRAPH FOR UNIFORM MOTION:-<\/span><\/u><\/strong><\/p>\r\n

                              \"VELOCITY-TIMEVelocity time graph for uniform motion is a straight line parallel to time axis. The area under the velocity time graph gives the displacement of the particle. Consider any two points C & D on the line corresponding to time T<\/span>1<\/sub><\/span>&T<\/span>2.<\/sub><\/span>Then the area of CDEF can be given as\u00a0<\/span><\/p>\r\n

                              Area of<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>CDEF= CD x CF = (<\/span>\"\") V<\/span>\u00a0\u00a0\u00a0<\/span>\u2013(i)<\/span><\/p>\r\n

                              As we know<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>V =\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\r\n

                              So from eqn (i)<\/span><\/p>\r\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Area of CDEF =\u00a0<\/span>\"\"=<\/span>\"\"\u00a0= displacement\u00a0<\/span><\/p>\r\n

                              Hence area under velocity time graph = displacement of the body.<\/span><\/p>\r\n

                              \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/strong><\/p>\r\n

                              12. Acceleration:-<\/span><\/u><\/strong><\/p>\r\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The rate of change of velocity is defined as the acceleration of the body<\/span>\u00a0\u00a0<\/span><\/p>\r\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>I,e<\/span>\u00a0\u00a0<\/span>a=<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\r\n