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. 0.2 Ns and 0.4 Ns0.4 Ns and 0.4 Ns0.8 Ns and 0.4 Ns0.8 Ns and 0.8 Ns

Solution

## The correct option is D 0.8 Ns and 0.8 Ns As we know velocity = slope of (x−t) 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|(vf−vi)| ∴ magnitude of impulse at t=2 s=|0.4(−1−1)|=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|(vf−vi)| ∴ magnitude of impulse at t=4 s=|0.4(1−(−1))|=0.8 Ns

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