Calculus Position Function

Question

 

The velocity in ft/sec of a particle is given by v(t) = -18t - 2. Find the position function s(t), of the particle if it has an initial position s(0) = 5 feet. (2 points)

Answer Choices:

A	-18t2 - 2t + 5
B	-9t2 - 2t - 5
C	-9t2 - 2t + 5
D	9t2 - 2t - 5

Answer 1

Integrate v(t) to find s(t):

v(t) = -18t - 2

s(t) = ∫v(t) = -9t² - 2t + C

Since s(0) = 5 feet, we can use the point (0,5) to solve for unknown constant C:

s(0) = 5 = -9(0)² - 2(0) + C

C = 5

Plug C into the equation for s(t):

s(t) = -9t² - 2t + C = -9t² - 2t + 5

Your answer is C