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.

Interpreting Different Sections in Distance-Time Graphs

• 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.

Calculating Speed from a Distance-Time Graph

• 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.