Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 17

The position of a particle moving along the x axis is given in centimeters by \(x = 9.75 + 1.50t^3\), where t is in seconds. Calculate (a) the average velocity during the time interval \(t = 2.00 \text{ s}\) to \(t = 3.00 \text{ s}\); (b) the instantaneous velocity at \(t = 2.00 \text{ s}\); (c) the instantaneous velocity at \(t = 3.00 \text{ s}\); (d) the instantaneous velocity at \(t = 2.50 \text{ s}\); and (e) the instantaneous velocity when the particle is midway between its positions at \(t = 2.00 \text{ s}\) and \(t = 3.00 \text{ s}\). (f) Graph x versus t and indicate your answers graphically.