Question

A runner travels 1.5 laps around a circular track in a time of 50 s. The diameter of the track is 40 m and its
circumference is 126 m. Find (a) the average speed of the runner and (b) the magnitude of the runner's
average velocity. Be careful here; average speed depends on the total distance traveled, whereas average
velocity depends on the displacement at the end of the particular journey.


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Answer 1

Answer:

The circumference is 126m - that is the distance around the track, so 1.5 laps is 126 times 1.5 = 189m

So he goes 189m in 50s. Distance = Rate * Time, Rate = Distance/Time

So his average speed is 189m/50s = 3.78 m/s

Answer 2

Given :

Laps taken , 1.5 .

Time taken , t = 50 s .

Diameter of track , d = 40 m .

Circumference , C = 126 m .

To Find :

a) The average speed .

b) The average velocity .

Solution :

We know , speed is given by :

$s=\dfrac{Distance }{Time }$

Here , distance covered is :

$d=126\times 1.5\ m\\d=189\ m$

Therefore , $s=\dfrac{189}{50}=3.78\ m/s$ .

Also , velocity is given by :

$v=\dfrac{Displacement}{time}$

Here , displacement is given by :

$D=126\times 0.5\\D=63\ m$

Therefore , velocity is :

$v=\dfrac{63}{50}\\\\v=1.26\ m/s$

Therefore , average speed and average velocity is 3.78 m/s and 1.26 m/s respectively .

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