Question

A body is acted on by a force given by $F=\left(15+3t^2\right)N$. The impulse received by the body during the first $2$ seconds is

• A. 28 Ns
• B. 38 Ns
• C. 30 Ns
• D. 19 Ns

Answer 1

Answer: (A)

Given,
Force, $F=\left(15+3t^2\right)N$
$\therefore$ Impulse, $I=\underset{0}{\overset{t}{\int }}F\cdot dt=\underset{0}{\overset{t}{\int }}\left(15+3t^2\right)dt$
For, $t=2s$
$I={\left[15t+3\times \frac{t^3}{3}\right]}_0^2$
$I=15\times 2+(2{)}^3=30+8=38Ns$