Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 71

In an arcade video game, a spot is programmed to move across the screen according to \( x = 9.00t - 0.750t^3 \), where \( x \) is distance in centimeters measured from the left edge of the screen and \( t \) is time in seconds. When the spot reaches a screen edge, at either \( x = 0 \) or \( x = 15.0 \text{ cm} \), \( t \) is reset to 0 and the spot starts moving again according to \( x(t) \). (a) At what time after starting is the spot instantaneously at rest? (b) At what value of \( x \) does this occur? (c) What is the spot's acceleration (including sign) when this occurs? (d) Is it moving right or left just prior to coming to rest? (e) Just after? (f) At what time \( t > 0 \) does it first reach an edge of the screen?