In an arcade video game, a spot is programmed to move across the screen accordin

Question

In an arcade video game, a spot is programmed to move across the screen according to x = 6.50t - 0.900t3, 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 = 18.0 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?
................ s

(b) Where does this occur?
................cm from the left edge

(c) What is its acceleration when this occurs?
................... cm/s2 (magnitude)


(d) In what direction is it moving just prior to coming to rest?


(e) In what direction is it moving just after coming to rest?


(f) When does it first reach an edge of the screen after t = 0?

Explanation / Answer

if the spot is instantaneously at rest, velocity =0 v= dx/dt = 8 + 2.25t^2 =0 t= 1.88 s. accn = d^2x/dt^2 = 8.46 m/s^2 x= 3.01 m . when this occurs. it is moving in the positive direction. to reach edge, x= 18 18 = 8t - 0.75t^3 solve for t. take the positive values.

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