Q1. The position of a pinewood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of the car for (a) the first second, (b) the last 3 s, and (c) the entire period of observation.
t (s) 0 1.0 2.0 3.0 4.0 5.0
x (m) 0 2.3 9.2 20.7 36.8 57.5
Q2. (a) Use the data in Problem 1 to construct a smooth graph of position versus time. (b) By constructing tangents to the x(t) curve, find the instantaneous velocity of the car at several instants. (c) Plot the instantaneous velocity versus time and, from this, determine the average acceleration of the car. (d) What was the initial velocity of the car?