Question

A train starting from rest is accelerated and the instantaneous acceleration is given by $\frac{10}{v+1}{m/s}^2$. Whwre $v$ is the velocity in $m/s$. Find the time after which the body attains a velocity of $54km/hr$.

• A. $10.75sec$
• B. $12.75sec$
• C. $12.25sec$
• D. $10sec$

Answer 1

The correct option is B $12.75sec$

Given $v=54km/hr=15m/s$,

$a=\frac{10}{v+1}$ $\Rightarrow \frac{dv}{dt}=\frac{10}{v+1}$

$\Rightarrow {\int }_0^{15}(v+1)dv={\int }_0^{t}10dt$

$\Rightarrow (\frac{v^2}{2}+v){|}_0^{15}=10t$ $\Rightarrow t=12.75$ $sec$