Question

A force $F_1$ accelerates a particle from rest to a velocity $v$. Another force $F_2$ decelerates the same particle from $v$ to rest, then

• A. $|F_1|$ is always equal to $|F_2|$
• B. $|F_2|$ is greater than to $|F_1|$
• C. $|F_2|$ may be smaller than, greater than or equal to $|F_1|$
• D. $|F_2|$ cannot be equal to $|F_1|$

Answer 1

The correct option is C $|F_2|$ may be smaller than, greater than or equal to $|F_1|$

From Newton's second law
$F_{net}=m\left(\frac{v-u}{t}\right)$
Case (i): Let time taken to accelerates a particle from rest to a velocity $v$ is $t_1$
Now $u=0,v=v$
$\Rightarrow F_1=\frac{mv}{t_1}$
Case (ii):Let time taken to decelerates the same particle from $v$ to rest is $t_2$
Here $u=v,v=0$
$\Rightarrow F_2=\frac{m(0-v)}{t_2}$
$F_2=\frac{-mv}{t_2}$
$F_1,F_2$ depends upon $t_1,t_2$. So, $F_2$ may be smaller than, greater than or equal to $F_1$.