An automobile initially moving at 30 ft/sec accelerates uniformly at 15 ft/sec^2. How fast is it moving after 3 sec.At the end of 3s the driver...

We'll have to write the equation that describes the
velocity of an object under acceleration.

v = v0 + a*t
(1)

We'll insert the given
informations:

v(3s) = 30 ft/s + (15
ft/s^2)(3s)

v(3s) = 30 ft/s + 45
ft/s

v(3s) = 75
ft/s

At the end of the interval of 3s, the
car is decelerated (the acceleration is opposite to the direction of
velocity).

v = 75 ft/s + (-30
ft/s^2)t

When the car comes to stop, v =
0.

0 = 75 ft/s + (-30
ft/s^2)t

-75 ft/s =
-30(ft/s^2)*t

t = 2.5
s

After 2.5 s, the car comes
to stop.