Step-by-step explanation:
To solve this problem, we can use the following formula for the distance (d) required to stop a car with uniform acceleration:
d = (v^2 - u^2) / (2a)
where v is the final velocity, u is the initial velocity, and a is the acceleration.
We are given that the car stops with uniform acceleration after its brakes are applied at a velocity of 80 mi/h and takes 400 ft to stop. Therefore, we can find the acceleration (a) as follows:
d = (v^2 - u^2) / (2a)
400 = (0 - 80^2) / (2a)
a = 6400 / (2 * 400)
a = 8 mi/h^2
We can now use this value of a to find the distance required to stop the car when its initial velocity is 40 mi/h.
Using the formula again, we get:
d = (v^2 - u^2) / (2a)
d = (0 - 40^2) / (2 * 8)
d = 800/16
d = 50 feet
Answer:
Therefore, the car will take 50 feet to stop under the same conditions when its initial velocity is 40 mi/h.