question_answer

  The   distance -time graph of two trains are given   below. The trains start simultaneously in the same direction,           (i) How much A is B ahead when the motion starts? (ii) What is the speed of B? (iii) When and where will A catch B? (iv)What is the difference between speeds of A and B? (iv) Is the speed of both the trains uniform or non-uniform? Justify your answer.

Answer:

                      (i) OA is a straight line graph between speed and time, and it is sloping upward from O to A.                                                                     (1/2) (ii) AB is a straight line graph between speed and time, which is parallel to the time axis (.v-axis). So, AB represents uniform speed. There is no acceleration from A to B.                            (1/2) (iii) BC is a straight line graph between speed and time which is sloping downwards from B to C. Therefore, BC represents uniform retardation or negative acceleration.                               (1) (iv) Acceleration of the body as we see from graph line OA represents it. So, the slope of     velocity-time graph OA will give the acceleration of the body. Thus, Acceleration = Slope of line we have, AD = 6 m/s, and OD = 4 s So, acceleration             (1) (v) The slope of line graph BC represents the   retardation of the body.                          So, retardation = Slope of line we have, BE = 6 m/s, EC = 16 -10 = 6 s Retardation                         (1)  (iv)The distance travelled by the body is equal to the area enclosed between the speed-time graph and time axis. Distance travelled from A to B = Area under the line AB and the time axis = Area of rectangle DABE = DA x DE Here, DA = 6 m/s and DE == 10 - 4 = 6 s Distance travelled from A to 5 = 6 x 6=36 m (1)