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Question

The figure shows the position-time (x-t) graph of one-dimensional motion of a particle of mass 0.4 kg. Find the magnitude of impulse imparted to the particle at t=2 s and 4 s respectively.


  1. 0.2 Ns and 0.4 Ns
  2. 0.4 Ns and 0.4 Ns
  3. 0.8 Ns and 0.4 Ns
  4. 0.8 Ns and 0.8 Ns


Solution

The correct option is D 0.8 Ns and 0.8 Ns

As we know velocity = slope of (xt) graph.
From graph 
For(0<t<2) s - particle has uniform velocity of vi=1 m/s.
For(2<t<4) s - particle has uniform velocity of vf=1 m/s.
At t=2 s velocity of particle is changing.

Using
Impulse (|J|)=|ΔP|=m|(vfvi)|
magnitude of impulse at t=2 s=|0.4(11)|=0.8 Ns

Simillarly,
For(2<t<4) s - particle has uniform velocity of vi=1 m/s.
For(4<t<6) s - particle has uniform velocity of vf=1 m/s.
At t=4 s velocity of particle is changing.
Using
Impulse (|J|)=|ΔP|=m|(vfvi)|
magnitude of impulse at t=4 s=|0.4(1(1))|=0.8 Ns

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