### Q.24:- Figure 5.17 shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body? What is the magnitude of each impulse?

**Answer:-**A ball rebounding between two walls located between at *x* = 0 and *x* = 2 cm; after every 2 s, the ball receives an impulse of magnitude 0.08 × 10^{–2} kg m/s from the walls

The given graph shows that a body changes its direction of motion after every 2 s. Physically, this situation can be visualized as a ball rebounding to and fro between two stationary walls situated between positions *x* = 0 and *x* = 2 cm. Since the slope of the *x*–*t* graph reverses after every 2 s, the ball collides with a wall after every 2 s. Therefore, ball receives an impulse after every 2 s.

Mass of the ball, *m* = 0.04 kg

The slope of the graph gives the velocity of the ball. Using the graph, we can calculate initial velocity (*u*) *as:u* = (2 – 0) × 10^{-2} / (2 – 0) = 10^{-2} m/s

Velocity of the ball before collision, *u* = 10^{–2} m/s

Velocity of the ball after collision, *v* = –10^{–2} m/s

(Here, the negative sign arises as the ball reverses its direction of motion.)

Magnitude of impulse = Change in momentum

= | mv – *mu* |

= | 0.04 (*v* – *u*) |

= | 0.04 (-10^{-2} – 10^{-2}) |

= 0.08 × 10^{-2} kg m/s