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?
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.