**Question 5.14:**

*t <*0

*, t >*4 s

*,*0

*< t <*4 s? (b) impulse at

*t =*0 and

*t =*4 s? (Consider one-dimensional motion only).

__Solution__:**(a)**

__For__

__t____< 0__

__For__

__t____> 4 s__

It can be observed from the given graph that the position of the particle is parallel to the time axis. It indicates that the particle is at rest at a distance of

3 m from the origin. Hence, no force is acting on the particle.

__For 0 <__

__t____< 4__

It can be observed that the given position-time graph has a constant slope. Hence, the acceleration produced in the particle is zero. Therefore, the force acting on the particle is zero.

**(b)**

__At__

__t____= 0__

Impulse = Change in momentum

=

*mv – mu*

Mass of the particle,

*m*= 4 kg

Initial velocity of the particle,

*u*= 0

Final velocity of the particle, v = 3 / 4 m/s

∴ Impulse = 4 ( 3/4 - 0) = 3 kg m/s

__At__

__t____= 4 s__

Initial velocity of the particle, u = 3 / 4 m/s

Final velocity o9f the particle,

*v*= 0

∴ Impulse = 4 (0 - 3/4) = -3 kg m/s

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