# Forces: Distance, Displacements, Speed and Velocity

## Forces: Distance and Displacement

### Definition of Distance and Displacement:

• Distance is a scalar quantity that describes the total path travelled by an object regardless of its direction.
• Displacement is a vector quantity and describes the shortest distance from the starting point to the finishing point, including a direction.

### Differences between Distance and Displacement:

• Distance is only concerned with how much ground an object has covered during its motion, while displacement also considers the direction of that motion.
• It is possible for an object to move a large distance but have a small or even zero displacement, for example in circular motion around a point.

## Forces: Speed

### Definition of Speed:

• Speed is the rate at which an object covers distance. It is a scalar quantity, meaning it does not include direction.
• It can be calculated by dividing the total distance travelled by the total time taken.

### Formula for Speed:

• The formula for calculating speed is: Speed (m/s) = Distance (m) / Time (s). That is, speed equals distance divided by time.
• High speed means that a large distance is covered in a short period of time.

## Forces: Velocity

### Definition of Velocity:

• Velocity is the speed of an object in a particular direction. It is a vector quantity, meaning it includes direction.
• Velocity can be calculated by dividing the displacement by the total time taken.

### Formula for Velocity:

• The formula for calculating velocity is: Velocity (m/s) = Displacement (m) / Time (s). That is, velocity equals displacement divided by time.
• Changing direction means changing velocity. Even if the speed remains the same, if an object changes direction, it has changed its velocity.

### Differences between Speed and Velocity:

• While both speed and velocity refer to how fast an object is moving, velocity also provides information about the direction of the motion, whereas speed does not.
• An object can travel at constant speed but still be accelerating if it is changing direction, because acceleration depends on velocity, not speed.

## Graphical Representation of Distance, Displacement, Speed and Velocity:

• In a distance-time graph, a horizontal line represents an object at rest. A sloping line indicates a steady speed, while a curving line represents acceleration.
• In a velocity-time graph, the slope of the line represents acceleration, a horizontal line represents constant velocity, and the area under the line represents displacement.
• Displacement-time and velocity-time graphs can be used to analyse and interpret motion.