question_answer

  An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 min 20s? Or Deduce the following equations of motion (i)          (ii)

Answer:

    (i) Diameter of circular track = 200 m                  Radius of circular track                 Circumference of circular track                                                                                                                                                                        (1)                 Total time given = 2 min 20 s                                 According to question, athlete takes 40 s to complete one round.                              Distance covered in 40                 (Distance covered in one round is equal to the circumference of the track).                 Distance covered inor distance covered in                                                                                                                                                                                                                              (1)                 (ii) As per the question, athlete completes one round in 40 s, i.e, after 40 s, athlete comes back to its initial position or after 40 s his displacement is zero.   Similarly   after   120 s , his displacement is zero.                                                                                                                                                                                                                 (1/2)                  Displacement after 2 min 20 s or 140 s                 = Displacement after 20 s.                                                                                                                                                            (1)                 (After 120 s (2 min), displacement is zero.)                                                                                                                                                                             (1/2)                 In 20 s, athlete will cover half the circular track from A to B (in 40 s one complete round is taken, so in 20 s half round will be taken).                 Displacement after 20 s = AB                 (Initial position is A and after half round, final position is B)                 = Diameter of circular track                 = 200 m                                                                                                                                                                                                (1) Or                 (i) Consider a body which starts with initial velocity u and due to uniform acceleration a, its final velocity becomes after time t. Then, its average velocity is given by                 Average velocity                                                                                                                                           (1)                 The distance covered by the body in time is given by                 Distance, s = average velocity time                 or                 or                                                                                                                                                 (ii) We know that,                                                                                      ?(i)                 Also,                                                                                                                                                            (1)                 Substituting the value of t in Eq. (i), we have                 or            or            or