Question

A force causes a stationary body of mass $12kg$ to be accelerated at a rate of $2m{s}^{-2}$ . If the final velocity of the body is $8m{s}^{-1}$, find the work done by the force.

• A. $360J$
• B. $384J$
• C. $396J$
• D. $420J$

Answer 1

The correct option is B $384J$

Given: mass of body, $m=12kg$, acceleration produced by force, $a=2m{s}^{-2}$, initial velocity, $u=0$ (body initially at rest), final velocity, $v=8m{s}^{-1}$.
Let the work done by force of magnitude $F$ be $W$.

Initial kinetic energy of the body: $=\frac{1}{2}m{v}^2=0$ (As the body is initially at rest)
Final kinetic energy of the body: $=\frac{1}{2}m{v}^2$
$\Rightarrow \frac{1}{2}\times 12\times 8^2=384J$

Now, work done = change in kinetic energy
i.e, work done = final K.E - initial K.E
$\Rightarrow (384-0)J=384J$
Therefore, the work done by the force is $384J$