NCERT Solutions
Class 11 Physics
Laws of Motion

Q. 4.14
Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for t < 0, t > 4 s, 0 < t < 4 s? (b) Impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only).
- At t<0, the particle is not moving so no force will act on it. For t >4, x has constant value of 3m.Therefore as the body is at rest therefore no force acting on it.
During the interval 0<t<4, according to given figure the body is moving with constant speed. Therefore there will be no acceleration as velocity of the particle is constant.
For t>4s, in the given graph, we can see that the position of the particle is parallel to the time axis. This shows the particle is at rest at a distance of 3 m from the origin. Hence, no force is acting on the particle.
- 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 = m/s
Therefore, Impulse =4( -0) =3kgm/s
At t = 4 s
Before t=4s, particle has a constant velocity. u=0.75m/s
Initial velocity of the particle, u= m/s
After t=4s, particle is at rest, i.e.
Final velocity of the particle, v = 0
Therefore, Impulse =4(0- ) = -3kgm/s