Forces: Distance-Time Graphs

Understanding Distance-Time Graphs

A Distance-Time Graph represents how an object moves over a period of time.
The horizontal axis (x-axis) usually represents time (t), whilst the vertical axis (y-axis) represents distance (d).
The gradient of the line on a distance-time graph represents speed. This can be calculated by dividing the change in distance by the change in time.
A horizontal line (zero gradient) on a distance-time graph indicates the object is stationary. The object’s distance from the starting point is not changing.
An uphill line (positive gradient) on a distance-time graph shows that the object is moving away from the start position. The steeper the line, the faster the object is moving.
A downhill line (negative gradient) is not valid on a distance-time graph because it would imply the object is moving backwards in time.
A curved line on a distance-time graph indicates the object is either accelerating or decelerating. Acceleration is seen by a steeper and increasing slope while deceleration is demonstrated by a shallower and decreasing slope.

To determine the distance travelled, look at the vertical axis of the graph.
To find out the time, check the horizontal axis.
The speed of the object at a specific time is the gradient of the line at that point.
For a straight diagonal line, the speed is constant, and the same at all points.
For a curved line, the speed is changing. The gradient of the tangent at a certain point will give you the speed at that instant.
To find out if an object is stationary, look for sections of the graph where the line is horizontal.

If the graph is one straight line, it suggests the object is moving at a constant speed.
If there are several straight lines with differing slopes, this indicates phases of different speeds.
A horizontal section represents a period of rest.
A curved section implies acceleration or deceleration.

Speed is calculated by dividing distance by time.
On a distance-time graph, this is done by measuring the gradient of the line, which is change in distance (vertical) divided by change in time (horizontal).
For a straight line this will give a single value for speed. For a curved line, the speed is constantly changing therefore you will need to work out the gradient (speed) at particular points.