The driver of a car going 86.0 km/h suddenly sees the lights of a barrier 44.0 m ahead. it takes the driver 0.75 s to apply the brakes, and the average acceleration during braking is -10.0 m/s2. (a) determine whether the car hits the barrier. (b) what is the maximum speed at which the car could be moving and not hit the barrier 44.0 m ahead? assume that the acceleration doesn't change.

Part a

NO

We need to calculate the distance traveled once the brakes are applied. Then we would compare the distance traveled and distance of the barrier.

Using the second equation of motion:

where s is the distance traveled, u is the initial velocity, t is the time taken and a is the acceleration.

It is given that, u=86.0 km/h=23.9 m/s, t=0.75 s,

Since there is sufficient distance between position where car would stop and the barrier, the car would not hit it.

Part b

29.6 m/s

The maximum distance that car can travel is

The acceleration is same,

The final velocity, v=0

Using the third equation of motion, we can find the maximum initial velocity for car to not hit the barrier:

Hence, the maximum speed at which car can travel and not hit the barrier is 29.6 m/s.