Question

When an object moves with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant? Explain.

Short answer

No, for constant velocity, the instantaneous velocity is equal to the average velocity.

Step-by-step solution

Step 1. Meaning of constant velocity

When an object travels with constant velocity, its magnitude and direction do not vary. The object travels with a uniform velocity when there is no variation between the average velocities in a time interval and the instantaneous velocity at any instant.

Step 2. Example for instantaneous velocity

Let the displacements in times $t_1$and $t_2$be $x_1$and $x_2$, respectively. Let $v$be the instantaneous velocity.

The expressions for displacements $x_1$and $x_2$are:

$\begin{array}{c}{x}_1=v{t}_1\\ x_2=v{t}_2\end{array}$

The expression for the average velocity is:

$\begin{array}{c}\overline{v}=\frac{x_1+x_2}{t_1+t_2}\\ =\frac{v{t}_1+v{t}_2}{t_1+t_2}\\ =v\end{array}$

Thus, for constant velocity, the instantaneous velocity should equal the average velocity.