Solving Rectilinear Problems - Example Problem 2.3-3

 

A speeder in a car passes a parked police car. The speeder is driving at a constant velocity of 100 mph. It takes the policeman 3 seconds to react, at which time, he accelerates the police car at 20 ft/s² until he reaches a maximum velocity of 120 mph. The police car continues to travel at 120 mph until it overtakes the speeding car. Starting at the point when the speeder passes the police car, what distance does the police car have to travel before it overtakes the speeding car?

 

Given:

• v_car = 100 mph = constant
• a_police,1 = 20 ft/s²
• v_police,max = 120 mph
• t_react = 3 s

 

Find:

• s when s_police = s_car

 

Solution:

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Draw the a-t, v-t and s-t graphs for the car and policeman.