Question

A force $F$ is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of cart at $t=5\text{sec}$ is -

• A. $10\text{m/s}$
• B. $\text{Zero}$
• C. $2\text{m/s}$
• D. $8.33\text{m/s}$

Answer 1

The correct option is D $8.33\text{m/s}$

Parabola has equation: $F=k{t}^2$

$\Rightarrow 50=k(5{)}^2$

$\Rightarrow k=2$

$\therefore F=2t^2$

$\Rightarrow m\frac{dv}{dt}=2t^2$

$\Rightarrow 10{\int }_0^{v}dv=2{\int }_0^5{t}^{2}dt$

$\Rightarrow 10v=2{\left[\frac{t^3}{3}\right]}_0^5$

$\Rightarrow v=8.33\text{m/s}$

Hence , option $\left(B\right)$ is correct.