You are driving down the highway late one night at 20 m/s when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10m/s^2. How much distance is between you and the deer when you come to a stop? Using the information given above and the value for distance that you found above, determine the time required for you to stop once you press the brakes.

- Distance between car and the deer when the car stopped = 20 m

- The time required for you to stop once you press the brakes = less than 5 s in order not to hit the deer.

Explanation:

Using the equations of motion,

In the 0.5 s reaction time, we need to first calculate how far he has travelled in that time.

a = 0 m/s² (Since the car is travelling at constant velocity)

x = ?

Initial velocity = u = 20 m/s

x = ut + at²/2

x = 20*0.5 + 0 = 10 m

From that moment,

a = - 10 m/s²

u = initial velocity at the start of the deceleration = 10 m/s

v = final velocity = 0 m/s

x = ?

v² = u² + 2ax

0² = 10² + 2 (-10) (x)

20x = 100

x = 5 m

Total distance travelled from when the deer stepped onto the road = 10 + 5 = 15 m

Distance between car and the deer when the car stopped = 35 - 15 = 20 m

b) To determine the time required to stop once you step on the brakes

u = 10 m/s

t = ?

v = 0 m/s²

x = distance from when the brake was stepped on to the deer = 35 - 10 = 25 m

x = (u + v) t/2

25 = (10 + 0) t/2

10t = 50

t = 5 s

Meaning the time required to stop once you step on the brakes is less than 5s.