Question

A person jogs eight complete laps around a 400-m track in a total time of 14.8min . Calculate the average speed, in m/s. Calculate the average velocity, in m/s.

Answer 1

Concepts and reason

The concepts used to solve this problem are average speed and average velocity.

First, calculate the total distance covered by the person, after that use the expression of average speed to calculate the average speed of the person.

Calculate the average velocity of the person by using the expression of average velocity.

Fundamentals

Write the expression for average speed.

${\rm{Average speed}} = \frac{{{\rm{total distance}}}}{{{\rm{time}}}}$

Write the expression for average velocity.

${\rm{Average velocity}} = \frac{{{\rm{displacement}}}}{{{\rm{time}}}}$

Calculate the total distance covered by the person.

$\begin{array}{c}\\{\rm{total distance}} = 8\left( {400{\rm{ m}}} \right)\\\\ = 3200{\rm{ m}}\\\end{array}$

Write the expression for average speed of the person.

${\rm{Average speed}} = \frac{{{\rm{total distance}}}}{{{\rm{time}}}}$

Substitute $3200{\rm{ m}}$ for ${\rm{total distance}}$ and $14.8{\rm{ min}}$ for time.

$\begin{array}{c}\\{\rm{Average speed}} = \frac{{3200{\rm{ m}}}}{{\left( {14.8{\rm{ min}}} \right)\left( {60{\rm{ s}}} \right)}}\\\\ = \frac{{3200{\rm{ m}}}}{{888{\rm{ s}}}}\\\\ = 3.60{\rm{ m/s}}\\\end{array}$

Understand that the displacement of the person is zero because he completes the lap.

Write the expression for average velocity of the person.

${\rm{Average velocity}} = \frac{{{\rm{displacement}}}}{{{\rm{time}}}}$

Substitute $0{\rm{ m}}$ for ${\rm{displacement}}$ and $14.8{\rm{ min}}$ for time.

$\begin{array}{c}\\{\rm{Average velocity}} = \frac{{0{\rm{ m}}}}{{\left( {14.8{\rm{ min}}} \right)\left( {60{\rm{ s}}} \right)}}\\\\ = \frac{{0{\rm{ m}}}}{{888{\rm{ s}}}}\\\\ = 0{\rm{ m/s}}\\\end{array}$

Ans:

Average speed of the person is $3.60{\rm{ m/s}}$ .

The average velocity of the person is $0{\rm{ m/s}}$ .