Question

A force $F=2t^{2}$ is applied to the cart initially at rest. The speed of cart at $t=5 \, s$ is -

• A. $10ms^{- 1}$
• B. $8.33ms^{- 1}$
• C. $2ms^{- 1}$
• D. zero

Answer 1

Answer: (B)

$F=2t^{2}$
$\Rightarrow m\frac{d v}{d t}=2t^{2}$
$\Rightarrow 10\displaystyle \int _{0}^{v}dv=2\displaystyle \int _{0}^{5}t^{2}dt$
$\Rightarrow 10v=2\left(\frac{t^{3}}{3}\right)_{0}^{5}$
$\Rightarrow v=8.33ms^{- 1}$