Question

The minimum stopping distance for a car depends on the driver’s reaction time and the car’s acceleration when the brakes are applied. A 1000 kg car traveling on a level road at speed 18 m/s travels 15 m (due to driver’s reaction time) before braking starts and then skids with the wheels locked another 30 m. Answer the following questions concerning this stopping process. (Ignore air resistance and assume g = 10 m/s^2.)

a) What is the driver’s reaction time?

b)  How long did it take for the car to come to a complete stop: include both segments – the one when the car was still going at a constant speed, and the other one when the car brakes were applied?

c) Sketch a v(t) (I believe it is a velocity-time) graph for the car motion for the entire braking process of the car: from the moment the driver noticed danger to the moment the car completely stopped. Indicate relevant times and velocities on the graph.

d) Show that the magnitude of the net force acting on the car when the car was skidding was 5400 N.

I'm not sure how I should start this. If someone could explain and answer It would be great. (:

Answer 1

a)

Initial velocity of car

Distance traveled by car before applying brakes is in time .

Drivers reaction time is

b)

Time taken by car to stop after brakes are applied is .

Distance traveled by car after brakes are applied is starting with velocity until it stops

Acceleration of car during the time is

Using

Total time taken by car to stop is

c)Displacement equations:

for

for

Velocity equations:

for

for

d)

Magnitude of net force acting on the car when the car was skidding is

( modulus of acceleration is used since the magnitude of force is required)