Suppose a particle moves along a straight line.

Question

The position at time t is given by s(t) = 3t−2t 2 , t ≥ 0, where t is measured in seconds and s(t) is measured in meters. How far to the right on the straight line does the particle travel?

Answer 1

If the question is really, what's the farthest to the right the particle travels, then you need to maximize s(t). What are the steps for finding the maximum values of a function?

Answer 2

v(t) = s'(t) = 3 - 4t = 0; t = 3/4 s; s(3/4) = 9/4 - 9/8 = 9/8 m