Question

A man walks $7\,km$ in $2$ hours and $2\,km$ in $1$ hour.
(a) What is the man’s average speed for the whole journey?
(b) What is the man’s average velocity for the whole journey?

Answer 1

Hint: In this question we have to find the average speed and average velocity. We will first find the total distance travelled by man by adding the distances and then we will calculate the total time taken by the man.

Formula used:
The formula of average speed is $\dfrac{D}{T}$, where $D$ is the total distance covered and $T$ is the total time taken.
We can calculate the average velocity by the formula: $\dfrac{\text{Total Displacement}}{\text{Total time}}$

Complete step by step answer:
(a) We have been given that a man walks $7km$ in $2$ hours and later he walks $2km$ in $1$ hour. Let us calculate the total distance travelled by man i.e.
$7 + 2 = 9km$
Now we will calculate the total time taken by him to travel:
$2 + 1 = 3hrs$
We know the formula of average speed i.e. $\dfrac{D}{T}$.
By putting the values in the formula we have:
$\text{Average speed} = \dfrac{9}{3}$
It gives us average speed of the man: $3km/hr$

(b) We will calculate the average velocity with the formula: $\dfrac{\text{Total Displacement}}{\text{Total time}}$
Average velocity of the man is calculated by dividing the total distance covered by man in one direction by the total time taken by him. Now we can see that average velocity will be the same as the average speed in this case since there is no direction mentioned in the question, or we can assume that both the distances are travelled in the same direction.
Therefore we can write that ;
Total displacement $ = $ total distance$ = 9km$
By applying the formula and putting the value we can write:
Average velocity= $\dfrac{9}{3}\,km/hr$

Hence the average speed of the man is $3km/hr$ and average velocity of the man is $3km/hr$.

Note: We should know that speed is defined as the rate at which an object is moving. So the average speed of a body in a certain time interval is the distance covered by the body in that time interval divided by time. We should note that speed is a scalar quantity as it only defines the magnitude, not the direction whereas, velocity is a vector quantity. It depends on both magnitude and direction.