__Question 5.24__:

__Solution__:*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) X 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 X 10

^{-2}kg m/s

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