Question

A body sliding on a smooth inclined plane requires $4\text{s}$ to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth of the distance starting from rest at the top?

• A. $1\text{s}$
• B. $2\text{s}$
• C. $4\text{s}$
• D. $16\text{s}$

Answer 1

The correct option is B $2\text{s}$

As the body takes $4s$ to reach the bottom from the top, let the distance covered by it be $l$.

Using 2nd equation of kinematics:
$s=ut+\frac{1}{2}a{t}^2$, here $u=0,s=l$
$l=\frac{1}{2}a(4{)}^2$
$\Rightarrow a=l/8$

Now lets say, body takes $t^{\prime }$ time to cover one-fourth distance from the top. Then,
$\frac{l}{4}=\frac{1}{2}a(t^{\prime }{)}^2$
$\frac{l}{4}=\frac{1}{2}.\frac{l}{8}.(t^{\prime }{)}^2$
$\Rightarrow (t^{\prime }{)}^2=4$
$t=2s$