the brakes of a car provide an acceleration of -5.0 m/s^2 . how long will it take for a car traveling at 20.0 m/s to stop ?

4-seconds.

But if you need to see the math, here you go:

Vf=Vi+at

Where

Vf=0m/s
Vi=20m/s
a=-5.0m/s
and
t=??

Solve for t:

0m/s=20m/s+(-5.0m/s^2)*t

-20m/s=(-5.0m/s^2)*t

t=-20m/s/-5.0m/s^2

t=4s

To find out how long it will take for a car to stop, we need to use the equation of motion:

v = u + at

Where:
v = final velocity (0 m/s)
u = initial velocity (20.0 m/s)
a = acceleration (-5.0 m/s^2)
t = time (unknown)

Rearranging the equation, we get:

t = (v - u) / a

Substituting the given values, we have:

t = (0 - 20.0) / -5.0

Calculating this expression gives us:

t = -20.0 / -5.0
t = 4.0 seconds

Therefore, it will take 4.0 seconds for the car traveling at 20.0 m/s to stop.