Question

Velocity of a particle of mass 2 Kg varies with time t according to the equation $v=(2t\hat{i}+4\hat{j})$ m/s. Here t is in seconds. Find the impulse imparted to the particle in the time interval from t = 0 to t = 2s.

Answer 1

Given,

Velocity, $v=(2t\hat{i}+4\hat{j})$

Change in velocity at time$(t=2\sec andt=0)$, $\Delta v=v_{t=2}-v_{t=0}=(4\hat{i}+4\hat{j})-4\hat{j}=4\hat{i}$.

Impulse, $I=F.\Delta t=m\Delta v=2\times 4\hat{i}=8\hat{i}$

Hence, impulses is $8\hat{i}$