Chapter 2, Problem 1FTD

Under what conditions are average and instantaneous velocity equal?

To determine

To provide: The conditions at which average velocity and instantaneous velocity are equal.

Explanation of Solution

Provide the formula for average velocity as shown below.

$\overline{v}=\frac{\Delta x}{\Delta t}$

Here, $\Delta x$ is the displacement and $\Delta t$ is the time interval.

Provide the formula for instantaneous velocity as shown below.

$v=\frac{dx}{dt}$

Here, $dx$ and $dt$ are the infinitesimals.

The average velocity and instantaneous velocity are equal when the acceleration is zero.