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Question

The position (x) - time (t) graph for a particle of mass 1kg moving along x-axis is shown in figure. Find impulse on particle at t=4s.
1232043_cfcd89c0c1b94b2ab1e87cd290e8dbca.png

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Solution

Velocity is nothing but the slope of xt graph, so the velocity just before t=4 will be
V1=slope=(200)m(40)sec=5m/sec
the velocity just after t=4 will be
V2=slope=(020)m(84)sec=5m/sec
so the change in momentum at t=4sec will be ΔP=m(V2V1)=1kg(55)m/s=10Kgm/s
if considering only magnitude the impulse is 10Kgm/s or 10Nsec

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