Question

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

Speed $v=10m/s$

Distance to be covered $d=100m$

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

For car to win the race :

Time $t=10s$

Initial velocity $u=0$

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

Or $100=0+\frac{1}{2}a(10{)}^2$

$⟹a=2m/s^2$