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# Vectors Show Direction of Motion

by Ron Kurtus (revised 17 July 2014)

A **vector** is a handy geometric representation of motion that includes both the *magnitude* and the *direction* of the motion of an object. Motion without a specified direction is called a **scalar** quantity.

Vectors are designated by arrows, with the length indicating the relative magnitude of the motion.

The distance an object moves is a scalar quanity. The straight-line distance in a specific dierction is the dispalcement vector. The velocity of an object is a vector quantity that is the speed in a specific direction. Acceleration is a change in velocity with respect time.

Some questions you may have include:

- What is the difference between distance and displacement?
- What is the difference between speed and velocity?
- How does acceleration relate to velocity?

This lesson will answer those questions. Useful tool: Units Conversion

## Distance-Displacement

Distance is an indication of how far an object travels in any direction. The path may be straight or roundabout. Distance is considerd a scalar quantity.

How far an object moves in a specific direction is called its displacement. It is only in a striaght line from a beginning point.

Distance versus displacement vector

## Speed-Velocity

Speed concerns how fast an object travels in any direction or path. The path may be straight or roundabout. Speed is a scalar quanity.

Velocity is how fast an object moves in a specific direction. Motion is only in a striaght line from a beginning point.

Speed versus velocity vector

When you indicate the velocity of an object, you should state its direction.

## Acceleration

Acceleration is the change of velocity with respect to time. Since velocity is a vector, any change of an object's velocity in the line of motion is an acceleration. Also, any change of direction is also an acceleration. When you indicate the acceleration of an object, you should state its direction.

If the object is moving faster in the direction of motion, the acceleration vector is also in the direction of motion.

Acceleration causes object to move faster

If the object is moving slower in the direction of motion, the acceleration vector is opposite the direction of motion.

Opposite acceleration cuases object to move slower

Acceleration on a curved path is designated by a vector at an angle to the velocity vector.

Acceleration at an angle causes path to curve

**Note**: Although an object may move freely at some given velocity, a force must be applied to it for the object to accelerate. The direction of acceleration is the direction of the force vector.

## Summary

A vector is a geometric representation of motion that includes both the magnitude and the direction of the motion of an object. Motion without a specified direction is called a scalar quantity. Vectors are designated by arrows, with the length indicating the relative magnitude of the motion.

The distance an object moves is a scalar quanity. The straight-line distance in a specific dierction is the dispalcement vector. The velocity of an object is a vector quantity that is the speed in a specific direction. Acceleration is a change in velocity with respect time.

Think positively

## Resources and references

### Websites

**Vectors and Direction** - The Physics Classroom

### Books

**Top-rated books on the Physics of Motion**

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## Vectors Show Direction of Motion