An object has a constant acceleration of 40 ft/sec^2, an initial velocity of −20 ft/sec, and an initial position of 10 ft. Find the position function, s(t), describing the motion of the object.

Answer 1

d^2s/dt^2 = 40
ds/dt = 40 t + c
when t = 0, ds/dt = -20
so ds/dt = 40 t - 20
s = 20 t^2 -20 t + d
when t= 0, s = 10
so s = 20 t^2 - 20 t + 10