(C) From Answer 4
s(t) = −16t 2 + 40t + 96.
Then
s′(t) = −32t + 40,
which is zero if t = 5/4, and that yields maximum height, since s′′(t)
= −32.
(E) The velocity v(t) of the car is linear, since its acceleration is constant
and
(B) Since v = 100 − 20t, s = 100t − 10t^2 + C with s(0) = 0. So s(1) = 100
− 10 = 90 ft.
(B) Since v = −32t + v 0 and s = −16t^2 + v 0 t, we solve simultaneously:
These yield t = 5/2 and v 0 = 80 ft/sec.
(A) The odometer measures the total trip distance from time t = a to t = b
(whether the car moves forward or backward or reverses its direction one
or more times from t = a to t = b). This total distance is given exactly by
