Question

A particle of mass $5\text{kg}$ is initially at rest. A force starts acting on it along a fixed direction. The magnitude of the force changes with time as shown in the figure. Find the velocity of the particle at the end of $20\text{s}$.

• A. $10\text{m/s}$
• B. $50\text{m/s}$
• C. $100\text{m/s}$
• D. $20\text{m/s}$

Answer 1

The correct option is D $20\text{m/s}$

Impulse imparted by force is given by $J=\int F.dt$
i.e Impulse = area under the $F-t$ curve
$\Rightarrow J=(5\times 2)+(5\times 4)+(5\times 6)+(5\times 8)$
$\therefore J=100\text{N-s}$

Initial velocity $v_1=\text{0 m/s}$
$\because$ particle is at rest initially.
Let the velocity of the particle at the end of $20\text{s}$ be $v_2$
Impulse imparted $J=m\Delta v$
$\Rightarrow J=m(v_2-v_1)$
$\Rightarrow 100=5(v_2-0)$
$\therefore v_2=20\text{m/s}$