Question: For 0 ≤ t ≤ 10 seconds, a car moves along a straight line with velocity
v(t) = 2 + 10t ft/sec
(a) Graph v(t) and find the total distance the car has traveled between t = 0 and t = 10 seconds using the formula for the area of a trapezoid.
(b) Find the function s(t) that gives the position of the car as a function of time. Explain the meaning of any new constants.
(c) Use your function s(t) to find the total distance traveled by the car between t = 0 and t = 10 seconds. Compare with your answer in part (a).
(d) Explain how your answers to parts (a) and (c) relate to the Fundamental Theorem of Calculus