Average Speed and Average Velocity - Definition, Formula, Example, FAQs
Average speed and average velocity are two important concepts that help us understand how objects move. Although they may sound similar, they describe motion in different ways. Average speed tells us how fast an object travels by considering the total distance covered and the total time taken. It does not depend on direction. Average velocity, on the other hand, depends on displacement the shortest distance between the starting and ending points and includes direction. These ideas form the base of motion and kinematics for students in Classes 9 and 11. In this article, we will clarify the difference between speed and velocity show you how to determine both, and bring examples for better understanding.
This Story also Contains
- What is Average Speed?
- What is Average Velocity?
- Difference Between Average Speed and Average Velocity
- Solved Examples – Average Speed & Average Velocity
What is Average Speed?
Average speed is defined as the total distance travelled divided by the total time taken to cover that distance. It represents the overall rate of motion, without accounting for changes in speed during the journey.
The formula for average speed is:
$
\text { Average Speed }=\frac{\text { Total Distance }}{\text { Total Time }}
$
Let's understand the concept of average speed by a numerical problem.
Example:
Rahul rode his motorcycle from Pune to Nagpur for two hours at 60 kmph and three hours at 70 kmph. Calculate average speed
Solution:
Distance covered at $60 \mathrm{~km} / \mathrm{h}$ :$60 \times 2=120 \mathrm{~km}$
Distance covered at $70 \mathrm{~km} / \mathrm{h}$ :
$70 \times 3=210 \mathrm{~km}$
Total distance travelled:
$120+210=330 \mathrm{~km}$
Total time taken:
$2+3=5 \text { hours }$
Average speed: $\text { Average speed }=\frac{\text { Total distance }}{\text { Total time }}=\frac{330}{5}=66 \mathrm{~km} / \mathrm{h}$
Answer: Average speed $=66$ km/h
1. Average Speed for a Single Journey
When an object moves with the same speed throughout the journey:
$
\text { Average Speed }=\frac{\text { Total Distance }}{\text { Total Time }}
$
2. Average Speed for Different Distances at Different Speeds
If different parts of the journey have different distances and different speeds:
$
\text { Average Speed }=\frac{d_1+d_2+d_3+\ldots}{t_1+t_2+t_3+\ldots}
$
(Find time of each part using $t=\frac{d}{v}$ )
3. Average Speed for Equal Distances at Different Speeds
If the object covers equal distances (say $d$ each) at different speeds $v_1$ and $v_2$ :
$
\text { Average Speed }=\frac{2 v_1 v_2}{v_1+v_2}
$
(This is the harmonic mean of the two speeds.)
4. Average Speed for Round Trip (Going and Coming Back)
If the distance going and returning is the same, with speeds $v_1$ and $v_2$ :
$
\text { Average Speed }=\frac{2 v_1 v_2}{v_1+v_2}
$
(Same as equal-distance case.)
5. Average Speed When Time Spent at Each Speed is Equal
If the object spends equal time at two speeds $v_1$ and $v_2$ :
$
\text { Average Speed }=\frac{v_1+v_2}{2}
$
(This is the arithmetic mean.)
What is Average Velocity?
Average velocity is defined as the total displacement (change in position) divided by the total time taken. It is a vector quantity, meaning it has both magnitude and direction, and it indicates the overall direction and rate of motion.
The formula used to calculate average velocity is:
$
\text { Average Velocity }=\frac{\text { Total Displacement }}{\text { Total Time }}
$
The numerical examples below will help you understand the idea of average velocity.
Example:
On the x-axis, what is the average velocity of a person moving 7 meters in 4 seconds and 18 meters in 6 seconds?
Solution:
A person moves $\mathbf{7 ~ m}$ in $\mathbf{4 s}$ and then $\mathbf{1 8 ~ m}$ in $\mathbf{6 s}$ along the x-axis.
Total displacement $=7+18=25 \mathrm{~m}$
Total time taken $=4+6=10 \mathrm{~s}$
$\text { Average velocity }=\frac{\text { Total displacement }}{\text { Total time }}=\frac{25}{10}=2.5 \mathrm{~m} / \mathrm{s}$
Answer: Average velocity $=2.5 \mathrm{~m} / \mathrm{s}$
Related Topics,
Difference Between Average Speed and Average Velocity
| Average Speed | Average Velocity |
| Total distance travelled divided by total time taken. | Total displacement divided by total time taken. |
| It is a scalar quantity. | It is a vector quantity. |
| Depends on the actual path taken. | Depends only on initial and final position. |
| Cannot be zero unless the object does not move at all. | Can be zero even if the object has moved (when displacement = 0). |
| Always positive. | Can be positive, negative, or zero. |
| Example: A car covering 100 km in 2 hours → Avg speed = 50 km/h. | Example: If a person returns to the starting point → Avg velocity = 0. |
Solved Examples – Average Speed & Average Velocity
Q.1 A person walks 600 m in 6 minutes and then 400 m in 4 minutes. Find his average speed.
Solution:
Total distance $=600 \mathrm{~m}+400 \mathrm{~m}=1000 \mathrm{~m}$
Total time $=6 \mathrm{~min}+4 \mathrm{~min}=10 \mathrm{~min}=600 \mathrm{~s}$
$
\text { Average speed }=\frac{\text { Total distance }}{\text { Total time }}=\frac{1000}{600}=1.67 \mathrm{~m} / \mathrm{s}
$
Answer: $\mathbf{1 . 6 7 ~ m} \boldsymbol{/} \mathbf{s}$
Q.2 A man moves 20 m east and then 10 m west in 6 seconds. Find his average velocity.
Solution:
Displacement = $20 \mathrm{~m}-10 \mathrm{~m}=10 \mathrm{~m}$ (east)
Total time $=\mathbf{6 ~ s}$
$
\text { Average velocity }=\frac{\text { Displacement }}{\text { Total time }}=\frac{10}{6}=1.67 \mathrm{~m} / \mathrm{s} \text { (east) }
$
Answer: $\mathbf{1 . 6 7 ~ m} / \mathbf{s}$ east
Q.3 A car travels the first 40 km at $50 \mathrm{~km} / \mathrm{h}$ and the next 60 km at $30 \mathrm{~km} / \mathrm{h}$. Find the average speed.
Solution:
Total distance $=40+60=100 \mathrm{~km}$
Time for first part $=40 / 50=0.8 \mathrm{~h}$
Time for second part $=60 / 30=2 \mathrm{~h}$
Total time $=0.8+2=2.8 \mathrm{~h}$
$
\text { Average speed }=\frac{100}{2.8}=35.7 \mathrm{~km} / \mathrm{h}
$
Answer: $\mathbf{3 5 . 7 ~ k m} \boldsymbol{/} \mathbf{h}$
Frequently Asked Questions (FAQs)
Because displacement is always less than or equal to the distance travelled, the magnitude of average velocity is always less than or equal to the average speed. The formula V = D/t is used to calculate average velocity, where V equals average velocity, D equals total displacement, and t equals total time.
The formula V = D/t is used to calculate average velocity, where V equals average velocity, D equals total displacement, and t equals total time.
Anything will accelerate as a result of forces acting on it. The object's velocity changes as a result of this acceleration. As a result, the initial velocity is the object's velocity before acceleration, which produces the change.
Velocity is a physical vector quantity that requires both magnitude and direction to define. Speed is a coherent derived unit whose quantity is measured in the SI (metric system) as meter per second (m/s or ms^-1).
For example, we might say that a car travels at 25 miles per hour on average. Due east, its average velocity could be 25 miles per hour. The rate of change in distance with respect to time can be thought of as average speed.