Speed-Time Graphs (Cambridge (CIE) IGCSE 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 speed

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

Motion on a speed-time graph

• The gradient of a speed-time graph (opens in a new tab) 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 smaller 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

Plotting a speed-time graph

• Follow these steps to plot a speed-time graph from data:

  1. Label the x-axis with time and the y-axis with speed

  2. Choose sensible scales so that the graph occupies more than half of the graph grid

  3. Use the data given to plot points on the graph

  4. Join the points with horizontal straight lines if the speed is constant, or sloped straight lines if the speed is not constant

Using 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