Mechanics Question - Finding speed reduction time

Question

A car of mass 1000 kg has its speed reduced from 81 km/h to 54 km/h by brakes
producing a force of 1250 N. How long does this take? Determine the work done by
the brakes on the car. Determine dependence on time of the power applied to the car.

Answer 1

An impulse is a force applied for a given time:

 

F·Δt = Δp

• F = applied force = -1250 newtons
• Δt = time the force is applied
• Δp = change in momentum

 

Solve for Δt.  Note that the change in momentum is mv_f - mv_i where m is the car's mass = 1000 kg and v_f and v_i are the car's final and initial speeds.  Note that you must convert the speeds to m/s to be in consistent SI units.

 

The work done is:

 

W = F·d

• W = work done
• F = applied force = -1250 N
• d = distance traveled while force is applied

 

The distance is:

 

d = (1/2)(F/m)Δt² + v_iΔt

• F = applied force = -1250 N
• m = car's mass = 1000 kg
• Δt = time force is applied = your answer from above
• v_i = initial velocity = 81 km/hr converted to m/s