Question

A body of mass $10kg$ is acted upon by a force given by equation $F=(3t^2-30)$ Newtons. the initial velocity of the body is $10m/s$. The velocity of the body after $5secs$ is

• A. $4.5m/s$
• B. $6m/s$
• C. $7.5m/s$
• D. $5m/s$

Answer 1

Answer: (C)

$7.5m/s$

$\begin{array}{c}\text{So Given force}=(3t^2-30)\\ \text{so accleration (a)}=\left(\frac{3t^2-30}{10}\right)m/s^2\\ a=\frac{dv}{dt}\end{array}$

$\begin{array}{c}adt=dv\\ 5\int \frac{3t^2-30}{10}dt={\int }_{10}^{v}v\\ {\text{vet final velocity be}}^{}{v}^{\prime }\end{array}$

$\begin{array}{cc}{\int }_0^5\frac{3t^3-30t}{3}& =v{|}_{10}^v\\ -\frac{25}{10}& =v-10\\ -\frac{25}{10}& =v-10\\ v& =+7.5m/s.\end{array}$

Ans C