Instantaneous Speed
- If an object’s speed is changing, then its distance-time graph will be a curve
- If it’s accelerating (speeding up), then the line will curve upwards
- If it’s decelerating (slowing down), then the line will curve downwards
- The speed at a particular time is found by calculating the gradient of a tangent to the curve, as shown in the image below:
Tangents are used to calculate the gradient at specific points on curved lines. On a distance-time graph, the gradient represents the speed of a moving object
- The tangent is a straight line that touches the curve at a particular point
- This point will be the time at which the speed is to be found
- The gradient of the tangent is then found from the same gradient equation:
Exam Tip
When you draw a tangent to a curve, make sure it just touches the point at which you wish to calculate the gradient. The angle between the curve and the tangent line should be roughly equal on both sides of the point.
