Question

A car and a bike start racing in a straight line. The distance of the finish line from the starting line is $100m$. The minimum acceleration of the car for it to win, if it accelerates uniformly starting from rest and the bike moves with a constant velocity of $10m/s$, is

• A. $0.5m/s^2$
• B. $2m/s^2$
• C. $1m/s^2$
• D. $3m/s^2$

Answer 1

The correct option is B $2m/s^2$

For bike :

Distance cover to finish the race $d=100m$

Velocity $v=10m/s$

Time taken $t=\frac{d}{v}=\frac{100}{10}=10s$

For car :

Let the acceleration be $a$.

Initial velocity of car $u=0$

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

where $t=10s$

So, $100=0+\frac{1}{2}\times a\times {10}^2$

$⟹a=2m/s^2$