A ball, initially at rest at seconds, rolls with constant acceleration down an inclined plane meters long. If the ball rolls meter in the first seconds, how far will it have rolled at seconds?
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The correct answer is . Since the initial speed of the ball is zero, distance down the plane as a function of time is related to acceleration by the equation
. The first condition, that the ball rolls meter in the first seconds, allows you to use this equation to determine that the acceleration is . Using the equation again with this acceleration and seconds gives a distance of meters. Alternatively, one could realize that since is proportional to , when the time is doubled the distance is quadrupled.