Question

A particle starts from rest at $t=0$ and undergoes an acceleration $a$ in $m{s}^{-2}$ with time $t$ in second which is as shown.
Calculate the particle's velocity at $2$ s, $3$ s, $4$ s

Answer 1

From the figure, we observe that:

(1)at $t=1$ seconds $u=0$ m/s and $a=3\text{m}/s^2$

We know $v=at+u=3\times 1=3m/s$

(2)At $t=2$ seconds $u=3$ m/s and acceleration $a=3\text{m}/s^{}$

$v=at+u=3\text{m}/s^2\times 2s+3m/s=9m/s$

(3)At $t=3$ seconds $u=9$ m/s and acceleration $a=-3\text{m}/s^2$

$v=-3m/s^2\times 3s+9m/s$

$v=0m/s$

(4)At $t=4$ seconds $u=0$ m/s and acceleration $a=-3\text{m}/s^2$

$v=-3m/s^2\times 4s+0m/s$

$v=-12\text{m/s}$