Question

a person is driving unsafely on the highway at a speed of 145km/h and has to slam on the brakes in order to avoid collision. the brakes can slow down the car at a rate of 10.4m/s^2. how far will the car travel while slowing down?

Answer 1

idk

Answer 2

To calculate the distance the car will travel while slowing down, we need to determine the time it takes for the car to come to a stop using the given deceleration rate.

First, we need to convert the car's speed from km/h to m/s:
145 km/h = 145,000 m/ (60 × 60) s = 40.28 m/s

We can use the formula:
acceleration = (final velocity - initial velocity) / time

Since the car is coming to a stop, the final velocity is 0 m/s and the initial velocity is 40.28 m/s. The deceleration rate is given as -10.4 m/s^2.

-10.4 m/s^2 = (0 m/s - 40.28 m/s) / time

Solving for time:
-10.4 m/s^2 × time = -40.28 m/s
time = -40.28 m/s / -10.4 m/s^2
time ≈ 3.88 seconds

Now, we can use the formula:
distance = initial velocity × time + (0.5 × acceleration × time^2)

distance = 40.28 m/s × 3.88 s + (0.5 × -10.4 m/s^2 × (3.88 s)^2)
distance ≈ 156.53 m

Therefore, the car will travel approximately 156.53 meters while slowing down.