Question

is average speed the magnitude of average velocity?

Answer 1

Answer on Question #38542, Physics, Other

Question:

Is average speed the magnitude of average velocity?

Answer:

Velocity is a vector, having both a direction and a magnitude (speed). Average speed equals:

$$v_a = \frac{\text{distance travelled}}{\text{time}}$$

and average velocity equals:

$$|\overrightarrow{v_a}| = \frac{\text{displacement}}{\text{time}}$$

Therefore average speed equals magnitude of average velocity only when distance equals displacement i.e. straight line motion in one direction

For example, let an object move with the speed of $v$ in positive direction during time $t$ and with the same speed $v$ during time $t$ in opposite direction. Then, displacement equals 0 and distance equals $2vt$. Therefore average speed is

$$v_a = \frac{2vt}{2t} = v$$

and average velocity is

$$|\overrightarrow{v_a}| = 0$$

which are not equal.