Question

A time varying force is represented as $F=2t\text{N}$. Find out the impulse imparted by this force during the first second.

• A. $\frac{1}{2}\text{N.s}$
• B. $1\text{N.s}$
• C. $2\text{N.s}$
• D. $4\text{N.s}$

Answer 1

The correct option is B $1\text{N.s}$

From the fundamental impulse theorem:
$J=\int Fdt$
Given, $F=2t\text{N}$ and limits for integration are $t=0\text{s}$ to $t=1\text{s}$
$\Rightarrow J={\int }_0^{1}2tdt$
$\Rightarrow J={[2\times \frac{t^2}{2}]}_0^1={\left[t^2\right]}_0^1$
$=(1-0)=1\text{N.s}$
$\therefore J=1\text{N.s}$