A ball is rolled up a ramp at 2.50 m/s. The ball slows down for 5.00 s and then rolls back down. Assume frictions isn't a factor and that the up ramp is the positive. At what point does the ball's acceleration change and what is the acceleration on the way down?
To determine the point at which the ball's acceleration changes and the acceleration on the way down, we need to analyze the given information.
First, let's break down the problem step by step:
1. The ball is rolled up the ramp at a speed of 2.50 m/s.
2. The ball slows down for 5.00 seconds.
3. The ball then rolls back down.
Based on the given information, we can infer that the ball will reach its highest point where its velocity becomes zero and then start descending.
Now let's calculate the point at which the ball's acceleration changes:
1. The initial speed of the ball when it rolls up the ramp is 2.50 m/s.
2. It slows down for 5.00 seconds, so its final velocity becomes zero.
3. We know that acceleration is defined as the change in velocity over time (∆v/∆t).
∆v = final velocity - initial velocity
Since the final velocity is zero, the change in velocity (∆v) is equal to the initial velocity of 2.50 m/s.
The time (∆t) during which the ball slows down is given as 5.00 seconds.
Therefore, the acceleration (a) can be calculated as:
a = ∆v/∆t = 2.50 m/s / 5.00 s = 0.50 m/s^2.
So, the acceleration changes direction when the ball slows down, and its acceleration is 0.50 m/s^2.
Next, let's calculate the acceleration on the way down:
Since friction is not a factor, the acceleration on the way down will be equal to the acceleration due to gravity (g) which is approximately 9.81 m/s^2 on Earth.
Therefore, the acceleration on the way down is 9.81 m/s^2.
In summary:
- The point at which the ball's acceleration changes is when the ball slows down after rolling up the ramp.
- The acceleration on the way down (assuming friction is not a factor) is equal to the acceleration due to gravity, which is approximately 9.81 m/s^2.