Distance-Time and Speed-Time Graphs

Distance-Time Graphs

Definition

A distance-time graph shows how an object’s motion changes with time.
The vertical axis (y-axis) represents the distance travelled and the horizontal axis (x-axis) represents the time taken.

Interpretation

Straight horizontal line: The object is stationary; it’s not moving.
Straight line sloping upwards: The object is moving at a constant speed. The steeper the line, the faster the speed.
Curved line: The object is accelerating or decelerating. The steeper the curve, the greater the acceleration.
The gradient of the line at any point on a distance-time graph represents the speed of the object.

Speed-Time Graphs

Definition

A speed-time graph shows how the speed of an object changes over time.
The vertical axis (y-axis) represents the speed and the horizontal axis (x-axis) represents the time.

Interpretation

Straight horizontal line: The object is moving at a constant speed.
Straight line sloping upwards: The object is accelerating. The steeper the line, the greater the acceleration.
Straight line sloping downwards: The object is decelerating. The steeper the line, the greater the deceleration.
Line returning to zero: The object is coming to a stop.
Area under a speed-time graph represents the total distance travelled.

Calculations

To calculate acceleration from a speed-time graph, use the formula: acceleration = (final speed - initial speed) / time
To calculate the distance travelled from a speed-time graph, calculate the area under the graph line. This can be done by visualising the graph as a series of shapes (usually triangles and rectangles) and finding their respective areas.

Remember, being able to correctly interpret and understand distance-time and speed-time graphs is essential for predicting an object’s future motion or understanding its previous motion.