Question

As the ball rolls up a slanted driveway with an initial velocity of 1.25 m/s, it travels upward, slowing down for 4.22 s, stops for an instant, and then rolls back down. What are the direction and the magnitude of the ball's acceleration as it rolls up the driveway?

A. Upward with magnitude 0.295 m/s²
B. Downward with magnitude 0.295 m/s²
C. Upward with magnitude 0.1475 m/s²
D. Downward with magnitude 0.1475 m/s²

Answer 1

The ball's acceleration as it rolls up the slanted driveway is downward, opposite to its initial motion, with a magnitude of 0.295 m/s². This results from using the kinematic formula to relate acceleration with the initial and final velocity over the given time.

Step-by-step explanation:

The direction and magnitude of the ball's acceleration as it rolls up the driveway can be determined by using the kinematic equations of motion. Given the initial velocity (v0) of 1.25 m/s, a final velocity (v) of 0 m/s (since the ball stops), and a time (t) of 4.22 s, we can use the equation v = v0 + at to find the acceleration (a).

Rearranging the equation to solve for acceleration, we get a = (v - v0) / t. Plugging in the values, a = (0 m/s - 1.25 m/s) / 4.22 s which gives an acceleration of approximately -0.295 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, so the ball is slowing down.

Therefore, the correct answer is:

• B. Downward with magnitude 0.295 m/s²