How far does the car travel before stopping?

Question

An automobile of mass 2 000 kg moving at 30 m/s is braked suddenly with a constant braking force of 10 000 N. How far does the car travel before stopping?

Answer 1

Use the kinematic relation

 

v_f² - v_i² = 2ax

 

v_f = final speed = 0 (full stop)

 

v_i = initial speed = 30 m/s

 

x = distance traveled

 

a = acceleration = F/m = force/mass

 

F = -10000 N (negative sign it it is opposing the direction of motion)

 

a = F/m = -10000 N / (2000 kg) = -5 m/s²

 

0 - v_i² = 2ax

 

x = -v_i² / 2a = [-(30²) / 2(-5)] m = 90 m