Question

A particle P moves along a straight line. At t1=3.0s the particle is at a point x1=8.0m at time t2=8.0s the prticle is at a point x2=-2.0m and at t3=12s the particle is at x3=2.0s find the average speed and average velocity and why are they not equal

Answer 1

$$v_s=\frac{|-2-8|+|2+2|}{12-3}=1.56\frac{m}{s}$$

$$v_v=\frac{2-8}{12-3}=-0.67\frac{m}{s}$$

In case the average speed is not equal to the magnitude of the average velocity, this is because the motion involves a change in direction and so path length is greater than the magnitude of displacement. So the average speed is greater than the magnitude of the velocity.