Question

A ball rolls from x = -5 m to x = 0 m in 1 second. What was its average velocity?(Units = m/s)

Don't forget: velocities and displacements to the right are +, to the left are -.

Answer 1

`5\; {\rm m\cdot s^(-1)}`.

Step-by-step explanation:

Displacement is the change in position. In this example, the position of this ball changed from the initial value of
`x_(0) = (-5)\; {\rm m}` to the final value
`x_(1) = 0\; {\rm m}`. Subtract the initial position from the final position to find the change in position:

`\begin{aligned} & (\text{Displacement}) \\ =\; & (\text{Change in Position}) \\ =\; & (\text{Final Position}) - (\text{Initial Position}) \\ =\; & 0\; {\rm m} - (-5)\; {\rm m} \\ =\; & 5\; {\rm m} \end{aligned}`.

Velocity is the rate of change in position. To find average velocity (average rate of change in position), divide the total change in position (displacement) by the time required for the change:

`\begin{aligned} & (\text{Average Velocity}) \\ =\; & \frac{(\text{Total Change in Position})}{(\text{Time Required})} \\ =\; & \frac{(\text{Displacement})}{(\text{Time Required})}\\ =\; & \frac{5\; {\rm m}}{1\; {\rm s}} \\ =\; & 5\; {\rm m\cdot s^(-1)} \end{aligned}`.

Therefore, the average velocity will be
`5\; {\rm m\cdot s^(-1)}`.