Average velocity is a central concept in Physics for understanding motion. Average velocity describes the rate at which an object changes its position in a specific direction over a certain period. While seemingly simple, this concept is a cornerstone in the realm of physics, playing a critical role in different fields.
In this article, we will look at the concept of average velocity, explore its calculation, and discuss its essential role in understanding the motion of objects in our universe.
What is Average Velocity in Physics?
Average velocity in physics refers to the total displacement (change in position) of an object over a given time period. It’s the total displacement divided by the total time.
Recall that velocity is a vector quantity, meaning it has both a magnitude (how fast the object is moving) and a direction (where the object is going). Just like velocity, average velocity is also a vector quantity – it has both a magnitude and a direction.
Average velocity is measured in units of distance over time, such as meters per second (m/s), miles per hour (mi/h) or kilometers per hour (km/h).
Typical Average Velocity of Common Objects
| Object | Velocity magnitudes |
|---|---|
| Human Walking | 1.4 m/s |
| Human Running | 5.5 m/s |
| Bicycle | 8 m/s |
| Racehorse | 15 m/s |
| Car (city driving) | 13.9 m/s (50 km/h) |
| Car (highway) | 27.8 m/s (100 km/h) |
| Cheetah | 30 m/s |
| High-Speed Train | 70 – 90 m/s |
| Commercial Jet Airplane | 250 – 260 m/s |
| Sound in Air (at sea level, 20°C) | 343 m/s |
| Space Shuttle (during launch) | 5,000 m/s |
The Difference Between Speed and Velocity
While speed and velocity are often used interchangeably in everyday language, in physics, they have distinct meanings. Speed is a scalar quantity referring only to “how fast an object is moving,” while velocity is a vector quantity that refers to “the speed of an object in a particular direction.”
Average Velocity Formula and Calculation
The average velocity of an object can be calculated by dividing the change in position by the time elapsed. The formula for calculating average velocity ($latex v_{av}$) is:
$$ v_{av} = \frac{\Delta x}{\Delta t}$$
where: $latex \Delta x$ is the displacement or change in position (final position – initial position) and $latex \Delta t$ is the change in time (final time – initial time).
In this formula, the displacement $latex \Delta x$ is measured in units of distance such as miles (mi), meters (m) or kilometers (km), while time ($latex \Delta t$) is measured in units like seconds (s), minutes (min), or hours (h).
The resulting average velocity ($latex v_{av}$) will then be in units of distance per unit time, like meters per second (m/s), kilometers per hour (km/h) or miles per hour (mi/h).
Calculating average velocity step-by-step
Here’s a step-by-step process of calculating average velocity:
- Calculate the displacement by subtracting the initial position from the final position.
- Find the change in time by subtracting the initial time from the final time.
- Divide the displacement by the change in time into the formula, and perform the division to find the average velocity.
Average Velocity – Examples with Answers
EXAMPLE 1
A car travels from a position of 0 km at time 0 hours, to a position of 120 km at time 2 hours. Find the average velocity.
Solution
We have the following:
- Initial position: 0 km
- Final position: 120 km
- Initial time 0 hours
- Final time: 2 hours
The displacement ($latex \Delta x$) is:
$latex 120 \text{ km} ~-~ 0 \text{ km} = 120 \text{ km}$
The change in time ($latex \Delta t$) is:
$latex 2 \text{ hours} – 0 \text{ hours} = 2 \text{ hours}$
Substituting these into the formula for average velocity:
$$ v_{av} = \frac{120 \text{ km}}{2 \text{ h}}$$
$latex v_{av} =60 ~\frac{\text{km}}{\text{h}}$
Thus, the car’s average velocity over this time period was 60 km/h.
EXAMPLE 2
A bike travels 300 meters to the east in 100 seconds, then 400 meters to the west in another 100 seconds. What is its average velocity?
Solution
The total displacement for the bike is:
$latex 300 \text{ m (east)}~ -~ 400 \text{ m (west)} = -100 \text{ m (west)}$
The time interval is:
$latex 100 \text{ s} + 100 \text{ s} = 200 \text{ s}$
Its average velocity is:
$$ v = \frac{-100 \text{ m}}{200 \text{ s}}$$
$latex v =-0.5 ~\frac{\text{m}}{\text{s}}$
The bike’s average velocity is -0.5 m/s in the x-axis.
EXAMPLE 3
A jogger runs 3 miles south in 30 minutes, then 4 miles north in 45 minutes. What is her average velocity?
Solution
For the jogger, the total displacement is:
$latex 4 \text{ mi (north)} ~- ~3 \text{ mi (south)} = 1 \text{ mi (north)}$
The total time is:
$latex 45 \text{ min} + 30 \text{ min} = 75 \text{ min}=1.25 \text{ h}$
The average velocity for the jogger is:
$$ v_{av} = \frac{1 \text{ mi}}{1.25 \text{ h}}$$
$latex v_{av} =0.8 ~\frac{\text{mi}}{\text{h}}$
The jogger’s average velocity was 0.8 mi/h in the y-axis.
EXAMPLE 4
An airplane flies 800 kilometers west in 2 hours, then 600 kilometers east in 1.5 hours. What is its average velocity?
Solution
The displacement ($latex \Delta x$) for the airplane is:
$latex 800 \text{ km (west)}~ -~ 600 \text{ km (east)} = 200 \text{ km (west)}$
The change in time ($latex \Delta t$) is:
$latex 2 \text{ h} + 1.5 \text{ h} = 3.5 \text{ h}$
The average velocity is:
$$ v_{av} = \frac{200 \text{ km}}{3.5 \text{ h}}$$
$latex v_{av} =57.14 ~\frac{\text{km}}{\text{h}}$
Thus, the airplane’s average velocity was 57.14 km/h to the west or -57.14 km/h in the x-axis.
Common Misconceptions About Average Velocity
One common mistake in understanding average velocity is equating it with average speed. As previously explained, velocity and speed are different; velocity takes into account the direction of movement, while speed does not. Consequently, it’s possible for an object to have a high average speed but a low or even zero average velocity if it ends up at its starting point, as the displacement would be zero.
Another misconception is that average velocity is always equivalent to the velocity at the midpoint of the time interval. This is not always true, particularly when an object’s motion isn’t uniform, i.e., its speed or direction changes during the time period.
To avoid these mistakes, it’s important to always remember that velocity is a vector. Remember that average velocity considers the total displacement (not total distance) and total time. And, while it may sometimes coincide with the midpoint velocity, this is not a rule and is dependent on the specifics of the motion.
See also
Interested in learning more about motion? Take a look at these pages:
Jefferson Huera Guzman
Jefferson is the lead author and administrator of Neurochispas.com. The interactive Mathematics and Physics content that I have created has helped many students.
