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Rates of Change : Velocity and Displacement

1.) Suppose a car starts from a stop sign and moves along a straight road. Assume the distance traveled in t seconds is given by s (t) + t^2 = 3t.
a.) How far has the car traveled after 5 seconds? [ find s(5) ]

b.) The speed of the car at exactly 10 seconds after "flooring it", can be estimated by finding the average speed over shorter and shorter time intervals. This speed can be found by finding the derivative of the function s(t). Find the speed at exactly 10 seconds after leaving the stop sign. [ Find s'(10) ]

2.) The distance in feet Mr. Nibble, a well known mouse form this area, was from the starting point of the maze is given by s(t) = 2t^2 - 5t + 40, where t is time in seconds.
a.) Find the average velocity of the mouse from this area, was from 2 seconds to 4 seconds. [ Find s(2) and s(4) then find the slope of the secant line ]

b.) Find the instantaneous velocity at 4 seconds. [Find s'(4) ]

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Rates of change, velocity and displacement are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.