Question

A class measured the velocity over time of a rolling ball relative to the surface it traveled on.

velocity of ball

time(s) velocity (m/s)
0 0
1 0.5
2 1.0
3 1.5
4 2.0
5 2.5

if the same acceleration were maintained over time, what velocity would the ball have relative to the surface it traveled on after 15 s?

Answer 1

To determine the velocity of the ball after 15 seconds, you can use the constant acceleration calculated from the data points provided. The ball accelerates at 0.5 m/s², leading to a final velocity of 7.5 m/s after 15 seconds.

Step-by-step explanation:

The student is asking about the velocity of a rolling ball after 15 seconds given a constant acceleration.

Since the table provided indicates a constant increase in velocity of 0.5 m/s every second, we can use this to find the velocity after 15 seconds.

The initial velocity is 0 m/s, and after 1 second it's 0.5 m/s, after 2 seconds it's 1 m/s, and so on. This pattern shows a linear increase, which implies a constant acceleration.

Assuming the acceleration is constant, at time t seconds, the velocity v in m/s can be calculated as v = at, with a being constant acceleration.

To calculate the acceleration, we can use any of the given velocity-time data points.

For example, at t = 1 second, v = 0.5 m/s, so a = v/t = 0.5 m/s².

Using this acceleration, the velocity after 15 seconds is v = a * t = 0.5 m/s² * 15 s = 7.5 m/s.

Therefore, the velocity of the ball relative to the surface it traveled on after 15 seconds would be 7.5 m/s, assuming the same acceleration is maintained over time.