Velocity is often used interchangeably with the scalar quantity of speed, but the two terms have distinct differences. Speed measures the distance traveled per unit of time and ignores the direction traveled. Velocity, however, is a vector quantity that considers change in position over time (magnitude) and offers a direction of movement. On a straight line without reversing course, speed and velocity are equivalent, but the real world is rarely that neat. Think of a 1-mile circumference race track. When a car crosses the finish line after 500 laps and two hours, it has traveled 500 miles at an average speed of 250 miles per hour. However, because the car ended at its original starting point, the magnitude of its average velocity is zero.

## Calculating Straight-Line Velocity

To calculate displacement on a graph or coordinate system, square the differences between each axis and take the square root of their sum. For example, on a two-dimensional graph from point (1,3) to point (5,5), the difference on the x-axis is 4, so its square is 16. The difference on the y-axis is 2, so its square is 4. Adding the two squared differences and taking the square root of the result gives you a positional change of 4.47 units.

Instantaneous velocity describes the magnitude of velocity at any point and uses the same formula as average velocity. The difference is that it uses a near-zero change in time to minimize the effects of averaging.

Another component of velocity is acceleration, which increases (or decreases) velocity at a given rate. To calculate the magnitude of the velocity at any point in time, multiply the constant acceleration rate times the time difference and then add it to the initial velocity. As an example, if you dropped a rock off a cliff, its velocity increases by 32 feet per second, every second. After 10 seconds, the velocity increases by 10 times 32 feet per second, or 320 fps.

Measure the change in position. On a straight line with a singular direction, this is simply the distance traveled. As an example, if you consistently drove due north from your home for 10 miles, the displacement is 10 miles. If you took a zigzag course to reach the same destination, the distance traveled would be greater, but the displacement would still be 10 miles. Therefore, be careful to measure the straight-line distance between two points when calculating the magnitude of velocity.

Measure the change in time. In the example, if you left home at 2 p.m. and arrived at your destination at 2:30 p.m., it took 30 minutes or 0.5 hours.

Divide the displacement by the change in time to calculate average velocity. In the example, divide 10 miles by 0.5 hours to calculate the average velocity of 20 miles per hour.

#### Tips

References

Tips

- To calculate displacement on a graph or coordinate system, square the differences between each axis and take the square root of their sum. For example, on a two-dimensional graph from point (1,3) to point (5,5), the difference on the x-axis is 4, so its square is 16. The difference on the y-axis is 2, so its square is 4. Adding the two squared differences and taking the square root of the result gives you a positional change of 4.47 units.
- Instantaneous velocity describes the magnitude of velocity at any point and uses the same formula as average velocity. The difference is that it uses a near-zero change in time to minimize the effects of averaging.
- Another component of velocity is acceleration, which increases (or decreases) velocity at a given rate. To calculate the magnitude of the velocity at any point in time, multiply the constant acceleration rate times the time difference and then add it to the initial velocity. As an example, if you dropped a rock off a cliff, its velocity increases by 32 feet per second, every second. After 10 seconds, the velocity increases by 10 times 32 feet per second, or 320 fps.