Question

Robbers in a car travelling at 20 $m{s}^{-1}$ pass a policeman on a motor cycle at rest.The policeman immediately starts chasing the robbers.The policeman accelerates at 3 $m{s}^{-2}$ for 12 s and thereafter travels at a constant velocity.Calculate the policeman before he overtakes the car.

• A. 250 m
• B. 300 m
• C. 270 m
• D. 280 m

Answer 1

The correct option is C 270 m

$u=0,t=12sec,\alpha =3m/s^2$

Distance covered by police in $12secs$

$s=ut+1/2a{t}^2\Rightarrow 0\times 12+1/2\left(3\right)(12{)}^2\Rightarrow 216mv=u+atv=36m/s$

Distance travelled by robber in $(12+t)sec$

Distance $=216+36t$

Speed $\times$ Time$=20(12+t)$

$2.16+36t=240+20t$

$t=1.5sec$

Total time $=12+1.5sec=13.5sec$

Distance $=216+36\left(1.5\right)=216+54=270m$