A girl drops a basketball off of a dam and it falls freely. Which of the following is true? The ball's kinetic energy increases by equal amounts in equal time intervals. The ball's kinetic energy increases by equal amounts in equal distances.
Question
A girl drops a basketball off of a dam and it falls freely. Which of the following is true? The ball's kinetic energy increases by equal amounts in equal time intervals. The ball's kinetic energy increases by equal amounts in equal distances.
Solution
The correct statement is: The ball's kinetic energy increases by equal amounts in equal time intervals.
Here's why:
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When the basketball is dropped, it starts with zero kinetic energy (since it's not moving). As it falls, it accelerates due to gravity.
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Kinetic energy is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. As the ball accelerates, its velocity (v) increases, which in turn increases its kinetic energy.
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The acceleration due to gravity is constant (ignoring air resistance), so the ball's velocity increases by equal amounts in equal time intervals. Therefore, the ball's kinetic energy also increases by equal amounts in equal time intervals.
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On the other hand, the ball's velocity (and therefore its kinetic energy) does not increase by equal amounts for equal distances fallen. This is because the ball is accelerating, so it covers each successive distance interval faster than the previous one. Therefore, the increases in kinetic energy are larger for later distance intervals.
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