Question

A time varying force $F=\left(2t\right)\hat{j}$ is acting on a particle of mass $m=3\text{kg}$ moving along y-axis. The velocity of particle is $-4\hat{j}\text{m/s}$ at time $t=0$. The velocity of the particle at the end of $4\text{s}$ is

• A. $4\hat{j}\text{m/s}$
• B. $-\frac{4}{3}\hat{j}\text{m/s}$
• C. $\frac{3}{4}\hat{j}\text{m/s}$
• D. $\frac{4}{3}\hat{j}\text{m/s}$

Answer 1

The correct option is D $\frac{4}{3}\hat{j}\text{m/s}$

Using, Impulse $\left(J\right)=\int Fdt=\Delta P$
$m(v_f-v_i)={\int }_0^{4}Fdt$

$v_f=\frac{1}{m}{\int }_0^4\left(F\right)dt+v_i$

$v_f=\frac{1}{3}{\int }_0^4\left(2t\right)\hat{j}dt-4\hat{j}$

$v_f=\frac{2}{3}\cdot {\left[\frac{t^2}{2}\right]}_0^4\hat{j}-4\hat{j}$
$=\frac{16}{3}\hat{j}-4\hat{j}=\frac{4}{3}\hat{j}\text{m/s}$