Question

A car moving on a road with uniform acceleration covers 20 m in the first second and 30 m in the next second.
What is its acceleration?

• A. $20m{s}^{-2}$
• B. $10m{s}^{-2}$
• C. $30m{s}^{-2}$
• D. $5m{s}^{-2}$

Answer 1

The correct option is B $10m{s}^{-2}$

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

Case 1 :

Distance covered $S=20m$

Time taken $t=1s$

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

Or $20=u\left(1\right)+\frac{1}{2}a(1{)}^2$

$⟹20=u+\frac{a}{2}$

We get $u=20-\frac{a}{2}$

Case 2 :

Total distance covered $S=20+30=50m$

Total time taken $t=1+1=2s$

So, $50=u\left(2\right)+\frac{1}{2}a(2{)}^2$

or $50=2u+2a$

Or $50=2(20-\frac{a}{2})+2a$

Or $50=40-a+2a$

$⟹a=10m/s^2$