Question

If a body travels $30m$ in an interval of $2s$ and $50m$ in the next interval of $2s$, then the acceleration of the body is

• A. $10m{s}^{-2}$
• B. $5m{s}^{-2}$
• C. $20m{s}^{-2}$
• D. $25m{s}^{-2}$

Answer 1

The correct option is B $5m{s}^{-2}$

Let initial velocity of the body is $u$ and acceleration is $a$.

Given, In first $2s$, $S=30m$,

Using $S=ut+\frac{1}{2}a{t}^2$ $\Rightarrow 30=u\times 2+\frac{1}{2}a\times 2^2$

$\Rightarrow u+a=15$ .....1

In next $2s$, Displacement$=50m$ $\Rightarrow t=4s$ , $S=30+50=80m$

$\Rightarrow 80=4u+\frac{1}{2}a\times 4^2$ $\Rightarrow u+2a=20$ ......2

Subtracting equation 1 from 2, $\Rightarrow a=5m/s^2$