Question

A body of mass $2kg$ moving on a horizontal surface with an initial velocity of $4m{s}^{-1}$, comes to rest after $2s$. If one wants to keep this body moving on the same surface with a velocity of $4m{s}^{-1}$, the force required is:

• A. zero
• B. $2N$
• C. $4N$
• D. $8N$

Answer 1

The correct option is C $4N$

Given:

Mass $m=2kg$

Initial velocity $u=4m{s}^{-1}$

Final velocity $v=0$

Time $t=2s$

The body comes to rest due to a retarding acceleration provided by a force, say $F_1$.

Let us calculate this acceleration by first equation of motion.

$v=u+at$

$\Rightarrow 0=4+a\left(2\right)$
$\Rightarrow a=\frac{-4}{2}=-2m/s^2$

By Newton's second law, the force providing this acceleration must be
$F_1=mass\times acceleration$

$\Rightarrow F_1=2\times -2=-4N$

Negative sign indicates the force is opposite to the velocity.

Now, to keep the body moving with the same velocity, the net force on the body must be zero. The force $F_2$ required to do so must be equal and opposite to $F_1.$

$F_2=-\left(F_1\right)=-(-4N)=+4N$

Option (C) is correct.