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?
Answers
idk
GPT 3.5
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.
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.