Question

1. the table below includes data for a ball rolling down a hill. fill in the missing data values in the table following the pattern that the existing data shows and determine the acceleration of the ball.

acceleration = _ m/s²

Explanation:

Step1: Find the change in velocity and time

From \(t = 0\) to \(t = 2\), the change in velocity \(\Delta v=3 - 0=3\ m/s\), and the change in time \(\Delta t = 2-0 = 2\ s\).

Step2: Calculate acceleration using the formula \(a=\frac{\Delta v}{\Delta t}\)

Substitute \(\Delta v = 3\ m/s\) and \(\Delta t=2\ s\) into the formula \(a=\frac{\Delta v}{\Delta t}\). So, \(a=\frac{3}{2}=1.5\ m/s^{2}\).
Let's check with another interval. From \(t = 2\) to \(t = 8\): \(\Delta t=8 - 2=6\ s\). The velocity at \(t = 2\) is \(3\ m/s\) and at \(t = 8\) is \(9\ m/s\). \(\Delta v=9 - 3=6\ m/s\). Then \(a=\frac{\Delta v}{\Delta t}=\frac{6}{6}=1.5\ m/s^{2}\). From \(t = 8\) to \(t = 10\): \(\Delta t=10 - 8 = 2\ s\), \(\Delta v=15-9 = 6\ m/s\), \(a=\frac{\Delta v}{\Delta t}=\frac{6}{2}=1.5\ m/s^{2}\)

Answer:

\(1.5\ m/s^{2}\)