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Explanation of Relative Motion, Speed, Velocity and Acceleration by Ron Kurtus - Succeed in Understanding Physics. **Key words:** physical science, relativity, point of reference, distance, rate, time, direction, deceleration, Ron Kurtus, School for Champions. Copyright © Restrictions

## Relative Motion, Speed, Velocity and Acceleration

by Ron Kurtus (revised 28 October 2007)

An object is in motion when it is continuously changing its position relative to a reference point and as observed by a person or detection device. For example, you can see that an automobile is moving with respect to the ground.

The distance the object goes in a period of time is its speed. If the speed of an object is in a specific direction, it is called velocity. The change in velocity over a period of time is the acceleration of the object.

Some questions you may have include:

- Why must motion be with respect to the observer?
- What is the difference between speed and velocity?
- Where is acceleration used?

This lesson will answer those questions.

Useful tool: Metric-English Conversion

## Motion is relative

All motion is relative to the observer or to some fixed object.

### Example with bus and car

For example, when you see a bus drive by, it is moving with respect to you. However, if you are in a car that is moving in the same direction, the bus will be moving at a different velocity with respect to you.

If your car is moving in the same direction and same speed as the bus, the bus will appear to not move with respect to you. Of course, if you compare the speed with the ground, both of you will be moving at some velocity.

Suppose you saw a person walking to the front of the moving bus. The person would be moving faster than the bus from your viewpoint. However, the person would not notice the speed of the bus while he walks to the front.

### Point of reference

In talking about motion, it is important to indicate your point of reference. In the case of moving automobiles, it is usually assumed the speed is with respect to the ground. But there are situations where the speed or velocity may be with respect to another object or an observer.

For example, suppose a car was traveling at 60 miles per hour (mph) and hit another car, but there was hardly a dent. The reason could be that the second car was traveling in the same direction at 59 mph, so the car was going only 1 mph with respect to the second car when it hit it.

### Sun looks like it is moving in the sky

Another example of relative motion is how the sun appears to move across the sky, when the earth is actually spinning and causing that apparent motion.

Usually, we consider motion with respect to the ground or the Earth. Within the Universe there is no real fixed point. The basis for Einstein's *Theory of Relativity* is that all motion is relative to what you define as a fixed point.

## Speed and velocity

**Speed** is how fast an object is going with respect to an object. **Velocity** is a measure of the speed *in a given direction*. You can say the top speed of an airplane is 300 kilometers per hour (kph). But its velocity is 300 kph in a northeast direction.

We distinguish between speed and velocity because if you add the speeds of objects, their directions are important. For example, the velocity of an airplane with respect to the ground would vary according to the direction of the wind.

### Measurement

In order to determine how fast an object is going, you measure the time it takes to cover a given distance, using the equation

d = vt

where:

**d**is the distance**v**is the speed or velocity**t**is the time covered**vt**is**v**times**t**

From this equation, you can get the equation for velocity as **v = d/t**. Velocity (**v**) or speed equals the distance (**d**) traveled divided by the time (**t**) it takes to go that distance.

### Example

For example, if a car went 120 miles in 2 hours, its average speed would be the distance of 120 miles divided by the time of 2 hours equaling 60 miles per hour (mph).

If it takes a car 2 minutes to travel 1 mile, its speed is 1 mile divided by 2 minutes, which equals 1/2 mile per minute or 30 miles per hour.

If you travel from Milwaukee to Chicago (90 miles) at an average velocity of 60 mph, it would take you 90 mi. ÷ 60 mph = 1.5 hours to travel the distance.

## Acceleration

Acceleration is the increase of velocity over a period of time. Deceleration is the decrease of velocity. When you start running, you accelerate (increase your velocity) until you reach a constant speed.

Mathematically, acceleration is the change in velocity divided by the time for the change

a = (v_{2}− v_{1})/(t_{2}− t_{1})

where:

**v**is the end velocity minus the beginning velocity_{2}− v_{1}**t**is the measured time period between the two velocities_{2}− t_{1}

Often this is written as **a = Δv/Δt**, where **Δ** is the Greek letter delta and stands for *difference*.

For example, if an object speeds up from a velocity of 240 meters/second to 560 meters/second in a time period of 10 seconds, the acceleration is (560 - 240)/10 = 320/10 = 32 m/s/s or 32 m/s².

Changing direction can also cause acceleration (or deceleration) because the velocity in that direction has changed.

## Summary

Motion is change in position. All motion is relative to some fixed point or object. Speed is a measurement of that change in position over time. Velocity is speed in a given direction. Acceleration is the increase in speed or velocity over a period of time. Deceleration is the decrease of speed or velocity over time.

Move; Do something; Excel

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## Relative Motion, Speed, Velocity and Acceleration