Motion on an Incline
In the following animation, a putted golf ball travels up a hill and then down again (position is given in meters and time is given in seconds). When an object (like a golf ball) travels up or down an inclined ramp or hill, its motion is often characterized by constant, non-zero acceleration. View the animation, then, answer the questions that follow. Click on the questions to review the explanations.
Click the image below to view the animation.
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How does the animation define the +x direction?
Down the hill—when the ball moves down the hill, it is moving in the +x direction and thus vx is positive. When the ball moves up the hill, it is moving in the -x direction and thus vx is negative.
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When is the ball slowing down? Speeding up?
Well, the answer to this question depends on what you mean by slowing down and speeding up. As the ball rolls up the hill its velocity is negative (because of how the x-axis is defined) and decreasing in magnitude (a smaller negative number). At the top of the hill, its velocity is zero, and as it travels down the hill, the ball is speeding up. Therefore, its speed decreases, reaches zero, and then increases. How can this be if vx is always increasing? Speed is the magnitude of velocity (and is always a positive number). As the ball travels up the hill, vx increases from -5 m/s to zero; yet its speed decreases from 5 m/s to zero. Note that the phrases "speeding up" and "slowing down" refer to how the speed changes, not necessarily to how the velocity changes.
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Is the acceleration of the golf ball increasing, decreasing, or constant?
To answer this, look at the slope of the graph at every instant of time. The slope of the velocity vs. time graph (velocity in the x direction) is equal to the acceleration (in the x direction). Does it change or is it the same? Notice that it is constant at all times and is in the positive x direction (as defined by the coordinates).
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