The position time graph of a body of mass 2 kg is as given in the figure. What is the impulse on the body at t – 0 sec and t = 4 sec.
The position time graph of a body of mass 2 kg is as given in the figure. What is the impulse on the body at t – 0 sec and t = 4 sec.

Mass of body, m = 2 kg

Time, t = 0

Initial velocity, v1 = 0

From graph, we know that

t ≥ 0 to t ≤ 4 which is a straight line.

The velocity of the body is constant

v2 = tan θ = 3/4 = 0.75 m/s

At t ≥ 4, the slope of the graph is zero so velocity v3 = 0

Impulse = Ft = (dp/dt)dt = dp

Impulse = change in momentum

Impulse at t = 0 is given as:

2(0.75 – 0) = 1.50 kg.m/s

Impulse at t = 4 is given as:

m(v3 – v2) = 2(0-0.75) = -1.50 kg.m/s

Impulse at t = 0 increases by +1.5 kg.m/s and at t = 4 it decreases by -1.5 kg.m/s.