A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of -2.0m/s^2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?

daliner4jl

daliner4jl

Answered question

2023-01-29

A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of 2.0 m / s 2 . How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?

Answer & Explanation

Miracle Hurley

Miracle Hurley

Beginner2023-01-30Added 9 answers

I'll begin with the distance traveled while slowing down. Since you know that the initial speed of the car is 15.0 m/s, and that its final speed must by 10.0 m/s, It is possible to calculate the distance travelled based on the given acceleration.
v f 2 = v i 2 - 2 a d
Isolate d on one side of the equation and solve by plugging your values
d = v i 2 - v f 2 2 a
d = ( 15.0 2 - 10.0 2 ) m 2 s - 2 2 2.0 m s - 2
d = 31.3 m
To get the time needed to reach this speed, i.e. 10.0 m/s, you can use the following equation
v f = v i - a t , which will get you
t = v i - v f a
t = ( 15.0 - 10.0 ) m s 2.0 m s 2 = 2.5 s

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