Speed-Time Graphs (Cambridge (CIE) IGCSE Co-ordinated Sciences (Double Award): Physics): Revision Note

Speed-time graphs

• A speed-time graph is used to describe the speed of an object and calculate its acceleration

Constant acceleration on a speed-time graph

• If an object is moving at a constant acceleration, the speed-time graph will be a straight line

  • If the constant acceleration is zero, the line will be horizontal

  • If the constant acceleration is non-zero, the line will have a gradient

• If an object has an acceleration of zero, the object is travelling at a constant velocity

  • Its velocity is not changing over time

  • If the constant speed is zero, then the object is stationary

Motion on a speed-time graph

This image shows how to interpret the slope of a speed-time graph

• The gradient of a speed-time graph represents the object's acceleration

  • A steeper slope, or a higher gradient, represents a greater acceleration

  • A shallower slope, or a lower gradient, represents a slower acceleration

• If the gradient is positive, the line slopes upward

  • A positive gradient represents an increasing speed, or acceleration

• If the gradient is negative, the line slopes downward

  • A negative gradient represents a decreasing speed, or deceleration

Speeding up and slowing down on a speed-time graph

Both of these objects are moving at a constant acceleration, because the lines are straight. The positive gradient represents an increasing speed or positive acceleration. The negative gradient represents a decreasing speed or negative acceleration.

Calculating distance from speed-time graphs

• Speed-time graphs can also be used to determine the distance travelled by an object

The area under a speed-time graph

• The area under a speed-time graph represents the distance travelled

The area under a speed-time graph represents the distance travelled

• If the area of a section of the speed-time graph forms a triangle, the area can be calculated using:

 $A_T=\frac{1}{2}bh$

• If the area of a section of the speed-time graph forms a rectangle, the area can be determined using:

 $A_R=bh$

• Where:

  • $A_T$ = area of a triangle

  • $A_R$ = area of a rectangle

  • $b$ = base

  • $h$ = height

• The total distance travelled can be determined by finding the total area under the speed-time graph

• The distance travelled for part of the journey can be determined by finding the area under the graph for a specific time interval

Area under a speed-time graph split into sections

The area under a speed-time graph can split into triangular and rectangular sections