describe 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

Assuming the object is traveling in a straight line (direction "s"), then s(t) = 10 - 20t + 1/2*40t² or, simplified,

s(t) = 10 - 20t + 20t² where t is in seconds and s is in feet

Answer 2

v(t)=∫a(t) dt = ∫40 ft/sec² dt = 40t + C

When t=0, v=-20 ft/sec

40(0) + C = -20 ft/sec

C=-20 ft/sec

s(t)=∫v(t) dt = ∫40t - 20 dt = 40t²/2 -20t + D

When t=0, s=10 ft

20(0)² -20(0) + D = 10 ft

D=10 ft

So the final function is:

s(t)=20t²-20t+10