Question

velocity and acceleration of a particle at time t=0 are $\overrightarrow{u}=(2\hat{i}+3\hat{j})$ m/s and $\overrightarrow{a}=(4\hat{i}+2\hat{j})m/s^2$ respectively. Find the velocity and displacement of particle at t=2 s.

Answer 1

Velocity of the particle at $t=2$ s $\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t$ where $t=2$ s

$\therefore$ $\overrightarrow{v}{|}_{t=2s}=(2\hat{i}+3\hat{j})+(4\hat{i}+2\hat{j})2=10\hat{i}+7\hat{j}$ $m/s$

Displacement of particle $\overrightarrow{S}=\overrightarrow{u}t+\frac{1}{2}\overrightarrow{a}{t}^2$

$\therefore$ $\overrightarrow{S}{|}_{t=2s}=(2\hat{i}+3\hat{j})\times 2+\frac{1}{2}\times (4\hat{i}+2\hat{j})\times 2^2=12\hat{i}+10\hat{j}$ $m/s^2$