A car applies the brakes and slows down from 15.0 m/s east to 5.00 m/s east in 4.00 s. What is the car's acceleration?

The acceleration of an object is simply the rate of change of velocity. It can also be written as,

a = dv/dt = (v2 - v1)/(t2 - t1)

here, a is the acceleration of the object, v1 and v2 are its velocities at time instants t1 and t2. 

In the given case, the object is traveling towards the east direction at 15 m/s initially. That is v1 is 15 m/s. The object's new velocity is 5 m/s, still due east, after 4 seconds. Thus, v2 is 5 m/s and the total time elapsed is 4 sec (= t2 - t1).

Hence, the acceleration of the object is given as:

a = (v2 - v1)/(t2 - t1) = (5 m/s - 15 m/s)/4 sec = (-10 m/s) / 4 sec

= - 2.50 m/s^2

Thus, the car is accelerating at -2.50 m/s^2 or, in other words, it is decelerating (negative acceleration) at 2.50 m/s^2.

Hope this helps.