The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.

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If an object moves along a straight line, the distance travelled can be represented by a distance-time graph.

In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

Calculate the speed of the object represented by the green line in the graph, from 0 to 4 s.

change in distance = (8 - 0) = 8 m

change in time = (4 - 0) = 4 s

\[speed = \frac{distance}{time}\]

\[speed = 8 \div 4\]

\[speed = 2~m/s\]

- Question
Calculate the speed of the object represented by the purple line in the graph.

change in distance = (10 - 0) = 10 m

change in time = (2 - 0) = 2 s

\[speed = \frac{distance}{time}\]

\[speed = 10 \div 2\]

\[speed = 5~m/s\]

If the speed of an object changes, it will be accelerating or decelerating. This can be shown as a curved line on a distance-time graph.

The table shows what each section of the graph represents:

Section of graph | Gradient | Speed |
---|---|---|

A | Increasing | Increasing |

B | Constant | Constant |

C | Decreasing | Decreasing |

D | Zero | Stationary (at rest) |

If an object is accelerating or decelerating, its speed can be calculated at any particular time by:

- drawing a tangent to the curve at that time
- measuring the gradient of the tangent

As the diagram shows, after drawing the tangent, work out the change in distance (A) and the change in time (B).

\[gradient = \frac{vertical~change (A)}{horizontal~change (B)}\]

It should also be noted that an object moving at a constant speed but changing direction continually is also accelerating. Velocity, a vector quantity, changes if either the magnitude or the direction changes. This is important when dealing with circular motion.