# Physics - representing motion

Additional Physics - Forces and Motion

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## Distance Time Graphs

The slope on a distance-time graph represents the speed of an object.

The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the acceleration of an object. The distance travelled is equal to the area under a velocity-time graph.

# Speed, distance and time

You should recall from your Key Stage 3 studies how to calculate the speed of an object from the distance travelled and the time taken.

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## The equation

When an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. This equation shows the relationship between speed, distance travelled and time taken:

• For example, a car travels 300 metres in 20 seconds.
• Its speed is 300 ÷ 20 = 15m/s.

Check your understanding of this topic by having a go at this activity.

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# Distance-time graphs

You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still.

## Background information

The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.

## Features of the graphs

When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped.

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# Velocity-time graphs

You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.

## Background information

The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.

The vertical axis of a velocity-time graph is the velocity of the object. The horizontal axis is the time from the start.

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## Features of the graphs

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. The steeper the line, the greater the acceleration of the object.

Notice that a line sloping downwards - with a negative gradient - represents an object with a constant deceleration - slowing down.

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# Acceleration

You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

## The equation

When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken:

• For example, a car accelerates in 5s from 25m/s to 35m/s.
• Its velocity changes by 35 - 25 = 10m/s.
• So its acceleration is 10 ÷ 5 = 2m/s2.
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# Distance-time graphs - higher

You should be able to calculate gradients on distance-time graphs.

## Background

To calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis.

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# Velocity-time graphs - higher

You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.

The gradient of a line on a velocity-time graph represents the acceleration of the object.

## Summary

• the gradient of a velocity-time graph represents the acceleration
• the area under a velocity-time graph represents the distance covered
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