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Question 28 of 36

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SAT Subject Test

A ball, initially at rest at t equals 0 seconds, rolls with constant acceleration down an inclined plane 10 meters long. If the ball rolls 1 meter in the first 2 seconds, how far will it have rolled at t equals 4 seconds?

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2 invisible times text  m end text

Correct Answer: 
No

3 invisible times text  m end text

Correct Answer: 
No

4 invisible times text  m end text

Correct Answer: 
Yes

5 invisible times text  m end text

Correct Answer: 
No

8 invisible times text  m end text

Correct Answer: 
No

The correct answer is 4 invisible times text m end text. Since the initial speed of the ball is zero, distance x down the plane as a function of time t is related to acceleration a by the equation
x equals 1 divided by 2 invisible times invisible times a t to the power of 2 end exponent. The first condition, that the ball rolls 1 meter in the first 2 seconds, allows you to use this equation to determine that the acceleration is 1 divided by 2 invisible times m divided by s to the power of 2 end exponent. Using the equation again with this acceleration and t equals 4 seconds gives a distance of 4 meters. Alternatively, one could realize that since x is proportional to t to the power of 2 end exponent, when the time is doubled the distance is quadrupled.

Question Difficulty: 
hard