Question

Alex is driving unsafely on the highway at a speed of 213km/h and has to slam on the brakes in order to avoid a collision. The brakes can slow down the car at a rate of 13.6m/s^2.
A) from the moment the car starts to slow down, how long will it take to stop?
B) how far will the car travel while slowing down?

Answer 1

To solve this problem, we can use the equations of motion.

A) To find the time it will take for the car to stop, we can use the equation:

v = u + at

Where:
v = final velocity (0 m/s since the car comes to a stop)
u = initial velocity (213 km/h = 213,000 m/3600 s = 59.17 m/s)
a = acceleration (-13.6 m/s^2)
t = time

Rearranging the equation to solve for time (t), we have:

t = (v - u) / a

Substituting the given values, we get:

t = (0 - 59.17) / -13.6
t ≈ 4.34 seconds

Therefore, it will take approximately 4.34 seconds for the car to stop.

B) To find the distance traveled by the car while slowing down, we can use the equation:

s = ut + (1/2)at^2

Where:
s = distance
u = initial velocity (59.17 m/s)
a = acceleration (-13.6 m/s^2)
t = time (4.34 seconds)

Substituting the given values, we get:

s = (59.17 * 4.34) + (1/2)(-13.6)(4.34)^2
s ≈ 128.2 meters

Therefore, the car will travel approximately 128.2 meters while slowing down.