Question

A cyclist moving on a circular track of radius 100 m completes one revolution in 4 minutes. What is his (i) Average speed (ii) Average velocity in one full revolution?​

Answer 1

▶ SOLUTION :

Given :

▪ A cyclist moving on a circular path of radius 100m completes one revolution in 4 minutes.

▪ No. of revolution = 1

To Find :

1. Average speed of the cyclist
2. Average velocity of the cyclist

Concept :

✴ Average speed is defined as the ratio of total distance travelked to the total time taken whereas average velocity is defined as the ratio of total displacement to the total time taken.

✴ Average speed is a scalar quantity.

✴ Average velocity is a vector quantity.

Calculation :

$\implies\sf\:av.\:speed=\dfrac{2\pi{R}}{t}\\ \\ \implies\sf\:av.\:speed=\dfrac{2\pi\times 100}{4\times 60}\\ \\ \implies\sf\:av.\:speed=\dfrac{628}{240}\\ \\ \implies\boxed{\bf{\pink{av.\:speed=2.61\:mps}}}\\ \\ \implies\sf\:Displacement\:after\:1\:revolution=0\\ \\ \implies\boxed{\bf{\green{av.\:velocity=0}}}$

Answer 2

GIVEN :

A cyclist moving on a circular track of radius 100 m completes one revolution in 4 minutes.

To FIND :

◾ (i) Average speed

◾(ii) Average velocity

FORMULA USED :

$\sf \: Average \: speed = \frac{total \: distance \: covered}{total \: time \: taken \: }$

$\sf \: Average \: velocity = \frac{total \: displacement}{total \: time}$

SOLUTION :

According to the question, the cyclist moves in a circular path so the total distance covered by it is the circumference of the circular path i.e 2¶r.

$\sf \: (i) \: Average \: speed= \frac{2\pi r}{t} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf \: \frac{2 \times 3.14 \times 100}{4 \times 60} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: = 2.61 \: m {s}^{ - 1}$

$\sf \: (ii) Average \: velocity = \frac{0}{4 \times 60} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: = 0 \: m {s}^{ - 1}$

As, displacement of the cyclist in the circular track is 0. So total displacement is 0 m. Hence, the average velocity of the cyclist in one full revolution is 0 ms¯¹.