A thief in a stolen car passes a police post at 90 km h⁻¹. A motorcycle cop reacts after 2 s, starts from rest with acceleration 5 m s⁻² and has maximum speed 108 km h⁻¹. Find the maximum separation between policeman and thief.
Options

Question

A thief in a stolen car passes a police post at 90 km h⁻¹. A motorcycle cop reacts after 2 s, starts from rest with acceleration 5 m s⁻² and has maximum speed 108 km h⁻¹. Find the maximum separation between policeman and thief.

Options

G1 Physics · Accepted Answer

Thief speed=25 m s⁻¹. During the 2 s reaction interval the lead becomes 50 m. After the cop starts, maximum separation occurs when cop speed reaches 25 m s⁻¹, after 5 s. In those 5 s, thief covers 125 m and cop covers (1/2)(5)(25)=62.5 m. Extra lead=62.5 m. Total=112.5 m. Option A.