Question

A car runs at a constant speed on a circular track of radius 300 m, taking time 62.8 seconds on each lap. Calculate the average speed and average velocity on each lap.

Answer 1

Step 1:Given data:

The radius of the track, R = 300 m.

Required time on each lap, t = 62.8 seconds.

Step 2:Finding the average velocity:

Displacement is the minimum distance of travel, it depends on the final and initial point of the path of travel, not the path connecting them. Thus the initial and final point of the circular track is coincides, that's why the minimum distance is zero.

For each lap of the circular track, the displacement is zero.

Now, $Averagevelocity=\frac{Totaldisplacement}{Totaltakentime}=0m/s.$

Therefore, the average velocity on each lap is zero.

Step 3:Finding the average speed:

The circumference(C) of the circular is given by,

$C=2\pi R$

Where ‘R’ is the radius of the circular path, $\mathrm{\pi }=\frac{22}{7}$

$C=2\mathrm{\pi R}=2\times \frac{22}{7}\times 300=1885.71m.$

Taking the formulae,

$Averagespeed=\frac{Totaldis\tan ce}{Totaltimetaken}=\frac{1885.71}{68.2}=27.65m/s.$

Therefore, the average speed on each lap is 27.65 m/s.