# 5.6.9 Instantaneous Speed

Higher Tier Only

### 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. ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
Close Close