Starting from an initial height h at time 0, a ball rolls down a frictionless in

Question

Starting from an initial height h at time 0, a ball rolls down a frictionless inclined plan, reaching a level surface at time t1. It rolls along the flat surface until time t2, when it begins rolling up a second inclined plane from time t2->t3. In this problem, you are asked to identify the correct sketches corresponding to velocity and acceleration in both the x- and y- directions (vx(t), ax(t), vy(t) and ay(t)). Which of the diagrams below best represent vx(t)? Which of the diagrams below best represent ax(t)? Which of the diagrams below best represent vy(t)? Which of the diagrams below best represent vy(t)? Which of the diagrams below best represent ay(t)?

Explanation / Answer

1) The third one; while the ball is rolling downhill, the velocity is increasing, when it rolls along the frictionless flat surface, there is no change in velocity and as it goes up the hill, velocity decreases until it reaches 0. 2) The second one; this one is simply the derivative of v(t) 3.1) (vx(t)) the third one; We know that the velocity in the x direction during the second time interval is constant and NOT 0, eliminating the first and second options. 3.2) (vy(t)) The first one; We know that the ball starts from rest, so that eliminates the third option. We also know that the acceleration in the y direction is always -9.81 for both the first and third time periods, making the slope of the vy(t) graph negative for those time periods. 4) The first one; we know there is no acceleration during the second time interval and that the acceleration during the first and third time intervals is -9.81.

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