Question

The displacement – time graph of a body of mass $2\text{kg}$ is shown. Find the impulse acting on the body in the time interval $t=2\text{sec}$ to $t=6\text{sec}$

• A. $2\sqrt{3}kgm/s$
• B. $(\sqrt{3}+1)kgm/s$
• C. $(\sqrt{3}-1)kgm/s$
• D. $2(\sqrt{3}-1)kgm/s$

Answer 1

The correct option is D $2(\sqrt{3}-1)kgm/s$

Mass of the body = $2kg$
We know that the slope of $x-t$ graph gives velocity.
At $t=2\text{sec}$
Velocity = $u=\frac{2}{2}=1m/s$
At $t=6\text{sec}$
Velocity, $v=\tan {60}^{\circ }=\sqrt{3}m/s$
Impulse = change in momentum = $(mv-mu)=2(\sqrt{3}-1)kgm/s$