The distance between two points A and B is 100 m. A person moves from A to B with a speed of $20m{s}^{-1}$ and comes back from B to A with a speed of $25m{s}^{-1}$.
Calculate the average speed and the average velocity of the person. [2 MARKS]

Average Speed : 1 Mark
Average Velocity : 1 Mark

Given, distance between A and B, $d=100m$
Person moves from A to B with a speed $v_1=20m{s}^{-1}$ and let the time taken be $t_1$.
He moves from B to A with a speed $v_2=25m{s}^{-1}$ and let the time taken be $t_2$
Total distance travelled $=2d=2\times 100=200m$
We know, $speed=\frac{distance}{time}\Rightarrow time=\frac{distance}{speed}$
$\therefore t_1=\frac{100}{20}=5s$ and $t_2=\frac{100}{25}=4s$
Total time taken, $t=t_1+t_2=5+4=9s$
We know, $averagespeed=\frac{totaldistance}{totaltime}=\frac{200}{9}=22.2m{s}^{-1}$
$Averagevelocity=\frac{totaldisplacement}{totaltime}$
Since the person starts from point A and comes back to point A, total displacement = 0.
Therefore average velocity = 0.