Question

A police car accelerates from rest (initial velocity is 0) at a rate of 5m/s² to catch a speeding car going 45m/s. How long does it take for the police car to catch the speeder? Assume the car is traveling at constant speed (0 acceleration) and that the two cars start at the same position.

Answer 1

answer) initial velocity of police

vi1=0m/s ( given)

acceleration of police

a_p=5m/s²

so from kinematics law we have

s ( police)=voi*t+1/2at²

s (police)=1/2*5*t²=2.5t²..............1)

now for the speeder

initial velocity=45m/s

and acceleration =0m/s²

so again we know the formula

s(speeder)=Vo*t+1/2*0t²

s( speeder)=45*t.........2)

when the police car catches the speeder than it means they have the same position

so s( police)=s(speeder)

2.5t²=45t

t=45/2.5

t=18s

so the answer is 18s