Question

A particle moving with a non-zero velocity and constant acceleration on straight line travels $15m$ in first $3s$ and $33m$ in next $3s$ in the same direction, find
(i) initial velocity of particle
(ii) acceleration of particle

Answer 1

Let initial velocity $u$ and acceleration $a$.

Using $s=ut+\frac{1}{2}a{t}^2$

$\Rightarrow 15=3u+\frac{1}{2}\times a\times 3^2$ $\Rightarrow 6u+9a=30$ .....1

Distance travelled in $6s$, $=15+33=48m$

$\Rightarrow 48=6u+\frac{1}{2}\times a\times 6^2$ $\Rightarrow 6u+18a=48$ .....2

Subtracting equation 1 from 2, we get $\Rightarrow 9a=18$ $\Rightarrow a=2m/s^2$

Put the value of $a=2$ in equation 1, we get $\Rightarrow u=2m/s$

Hence, Initial velocity $=2m/s$

Acceleration $=2m/s^2$