<p>This is a question from collegeboard's website </p>
<p>A ball, initially at rest at t= 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= 4 seconds?</p>
<p>(A) 2 m
(B) 3 m
(C) 4 m
(D) 5 m
(E) 8 m </p>
<p>This is the answer they put:</p>
<p>Correct Answer: C</p>
<p>Explanation:
The correct answer is 4 m. 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 = 1/2 a(t squared). 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 1/2 m/(s squared). Using the equation again with this acceleration and t = 4 seconds gives a distance of 4 meters. Alternatively, one could realize that since x is proportional to t squared, when the time is doubled the distance is quadrupled.</p>
<p>How come though if you do v2 (at 2.0s) = delta d / delta t = 1 m / 2.0 s you get v2 = 0.5 m/s then if you do a (acceleration) = delta v / delta t
= (v2-v1)/delta t = (0.5 m/s - 0 m/s) / 2.0 s
= acceleration of 0.25 m/(s squared) rather than the 0.5 m/(s squared they said). </p>
<p>Also, their calculations make sense but if you think about it at 2.0 seconds the ball obviously has a velocity of 0.5 m/s, but if the acceleration was
0.5 m/ (s squared) as they said, then at 2.0 seconds wouldn;t the velocity be 1.0 m/s rather than 0.5 m/s?</p>
<p>Can someone please clear up this matter and tell me what I am doing wrong or what collegeboard is doing wrong.</p>