A ball is rolled up an incline with a speed of 3.5 m/s. After it rolls for 2.2 s, it is located 1.9 mup the incline from where it started. Determine the acceleration of the ball.
Question
A ball is rolled up an incline with a speed of 3.5 m/s. After it rolls for 2.2 s, it is located 1.9 mup the incline from where it started. Determine the acceleration of the ball.
Solution
To solve this problem, we can use the following kinematic equation:
d = vit + 0.5at^2
where: d = displacement = 1.9 m vi = initial velocity = 3.5 m/s t = time = 2.2 s a = acceleration (which we are trying to find)
First, we need to solve for the term vit:
vit = vi * t = 3.5 m/s * 2.2 s = 7.7 m
Next, we subtract vit from d to solve for the term 0.5at^2:
0.5at^2 = d - vit = 1.9 m - 7.7 m = -5.8 m
Then, we divide this result by 0.5t^2 to solve for a:
a = 2(0.5at^2) / t^2 = 2(-5.8 m) / (2.2 s)^2 = -2.4 m/s^2
So, the acceleration of the ball is -2.4 m/s^2. The negative sign indicates that the acceleration is directed opposite to the direction of motion, which makes sense because the ball is rolling up the incline and slowing down.
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