Find the position function, s(t), describing the motion of the object.

Question

An object has a constant acceleration of 40 ft/sec², 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

a(t) = 40, integrate to find v(t)

v(t) = 40t+c, v(0)=-20

-20=40(0)+c; c=-20, v(t) = 40t-20, integrate to find s(t)

s(t) = 20t^2-20t+c, s(0)=10

10=20(0)-20(0)+c; c=10, so s(t) = 20t^2-20t+10