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?
Time needed: 2.5 s
Distance covered: 31.3 m
I'll start with the distance covered while decelerating. 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, you can use the known acceleration to determine the distance covered by
To get the time needed to reach this speed, i.e. 10.0 m/s, you can use the following equation
SIDE NOTE I left the value I got for the distance rounded to three sig figs.