(a) (i) For t < 0, the position time graph is AO which means displacement of the particle is zero, i.e. particle is at rest at the origin. Hence force on the particle must be zero.
(ii) For t > 4 s, the position time graph BC is parallel to time axis.
Therefore, the particle remains at a distance of 3 m from the origin, i.e., it is at rest. Hence force on the particle is zero.
(iii) For 0 < t < 4 s, the position time graph OB has a constant slope.
Therefore, velocity of the particle is constant in this interval i.e. particle has zero acceleration. Hence force on the particle must be zero.
(b) Impulse at t = 0
Impulse = change in linear momentum.
Before t = 0, particle is at rest i.e. u = 0.
After t = 0, particle has a constant velocity
∴ Impulse =m(v−u)=4(0.75−0)=3kg m s−1
Impulse at t=4 s
Before t=4s, particle has a constant velocity u=0.75ms–1After t=4s, particle is at rest i.e. v=0
∴ Impulse =m(v−u)=4(0−0.75)=−3kgm s−1