Question

A point initially at rest moves along $x$-axis. Its acceleration varies with time as $a=(61+5)$ in $m/s$. If it starts from origin, the distance covered in $2s$ is

• A. 20 m
• B. 18 m
• C. 16 m
• D. 25 m

Answer 1

Answer: (B)

Given, $a=\frac{dv}{dt}=6t+5$
$\underset{0}{\overset{v}{\int }}dv=\underset{0}{\overset{t}{\int }}(6t+5)dt$
$v=\frac{6t^2}{2}+5t$
$\frac{ds}{dt}=\left(\frac{6t^2}{2}+5t\right)dt$
$s=\frac{3t^2}{3}+\frac{5t^2}{2}$
where, $t=2s$,
$S=3\times \frac{2^3}{3}+\frac{5\times 2^2}{2}=18m$