Question

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.

Answer 1

Part a

Answer: 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:

`s=ut+0.5at^2`

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,
`a=-10.0 m/s^2`

`\Rightarrow s=23.9 m/s * 0.75s+0.5* (-10.0 m/s^2)* (0.75 s)^2=15.11 m`

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

Part b

Answer: 29.6 m/s

The maximum distance that car can travel is
`s=44.0 m`

The acceleration is same,
`a=-10.0 m/s^2`

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:

`v^2-u^2=2as`

`0-u^2=-2 \time 10.0m/s^2 * 44.0 m\Rightarrow u=√(880 m^2/s^2)=29.6 m/s`

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