Question

A person completes a round of circular track of radius 21 m in 4 s. Calculate his average speed and average velocity.​

Answer 1

Answer:

Provided that:

• Circular track is given.
• Time taken = 4 seconds
• Radius = 21 meters

To calculate:

• Average speed
• Average velocity

Solution:

• Average speed = 33 m/s
• Average velocity = 0 m/s

Using concepts:

• Average velocity formula
• Average speed formula
• Distance formula for circle

Using formulas:

• ${\small{\underline{\boxed{\pmb{\sf{A_{av} \: = \dfrac{s}{t}}}}}}}$

Where, A_{av} denotes average velocity, s denotes total displacement and t denotes total time.

• ${\small{\underline{\boxed{\pmb{\sf{v \: = \dfrac{s}{t}}}}}}}$

Where, v denotes average speed, s denotes total distance and t denotes total time taken.

Knowledge required:

• Displacement is the shortest distance between the initial and final positions.

Required solution:

~ Firstly let us find out the average speed by using the suitable formula!

$:\implies \sf v \: = \dfrac{s}{t} \\ \\ :\implies \sf v \: = \dfrac{2 \pi r}{t} \\ \\ :\implies \sf v \: = \dfrac{2 \times 22 \times 21}{7 \times 4} \\ \\ :\implies \sf v \: = \dfrac{44 \times 21}{28} \\ \\ :\implies \sf v \: = \dfrac{924}{28} \\ \\ :\implies \sf v \: = \cancel{\dfrac{924}{28}} \: (Cancelling) \\ \\ :\implies \sf v \: = 33 \: ms^{-1} \\ \\ :\implies \sf Average \: speed \: = 33 \: ms^{-1}$

• Therefore, average speed = 33 metre per second.

~ Now let's calculate the average velocity by using suitable concept!

Explanation: Here, the displacement is 0 m because the person take one round of circle and here the initial and final positions are same therefore, the displacement is zero here.

$:\implies \sf A_{av} \: = \dfrac{s}{t} \\ \\ :\implies \sf A_{av} \: = \dfrac{0}{4} \\ \\ :\implies \sf A_{av} \: = 0 \: ms^{-1} \\ \\ :\implies \sf Average \: velocity \: = 0 \: ms^{-1}$

• Henceforth, average velocity = 0 metre per second.