SolveItClass 9 · NCERT

NCERT Solutions · Class 9 Science Describing Motion Around Us

23 questions · 13 still being checked

Revise, Reflect, Refine 4.6–4.7 (part 11 of 13)

  1. Exercise 4.6

    Fig. 4.27\displaystyle 4.27 shows a position-time graph of two objects A and B that are moving along the parallel tracks in the same direction. Do objects A and B ever have equal velocity? Justify your answer. Position (m) 0\displaystyle 0NCERT_Question_Class9_Science_Ch4_RRR_Q4-6

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    NCERT’s answer
    No
    No — A and B never have equal velocity.
    Both graphs in Fig. $\displaystyle 4.27$ are straight lines, so each object moves with its own constant velocity throughout the motion.
    On a position-time graph the velocity is the slope of the line. The two lines have visibly different steepness, so the two constant velocities are different numbers — and being constant, they stay different at every instant.
    Where the two lines meet, A and B have the same position, i.e. they are side by side on their parallel tracks and one overtakes the other. Equal position is not equal velocity.

  2. Exercise 4.7

    A graph in Fig. 4.28\displaystyle 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0\displaystyle 0 to 10\displaystyle 10 seconds. Choose the correct option(s). (i) The average velocity of both over the 10\displaystyle 10 s time interval is equal since they have the same initial and final positions. (ii) The average speeds of both over the 10\displaystyle 10 s time interval are equal since both cover equal distance in equal time. (iii) The average speed of A over the 10\displaystyle 10 s time interval is lower than that of B since it covers a shorter distance than B in 10\displaystyle 10 seconds. (iv) The average speed of A over the 10\displaystyle 10 s time interval is greater than that of B since B’s speed is lower than A’s in some segments.NCERT_Question_Class9_Science_Ch4_RRR_Q4-7

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    NCERT’s answer
    (i)
    ; (ii)
    Correct options: (i) and (ii).
    (i) is true: both objects have the same initial position and the same final position, so both have the same displacement over the same \(\displaystyle 10\ \text{s} \); reading the graph, \(\displaystyle v_{av} = \frac{10\ \text{m}}{10\ \text{s}} = 1\ \text{m s}^{-1} \) for each.
    (ii) is true: neither graph ever falls, so neither object turns back. For one-way motion the distance travelled equals the magnitude of displacement, so each covers \(\displaystyle 10\ \text{m} \) and \(\displaystyle \text{average speed} = \frac{10\ \text{m}}{10\ \text{s}} = 1\ \text{m s}^{-1} \) for both.
    (iii) is false: A does not cover a shorter distance than B — both cover the same \(\displaystyle 10\ \text{m} \).
    (iv) is false: B is indeed slower than A over some stretches, but it is faster over others, and over the full \(\displaystyle 10\ \text{s} \) the two average out to the same speed.
    What really differs between A and B is their velocity at individual instants, not their averages over the whole interval.