Speed-Time Graphs (CIE IGCSE Physics)

• A speed-time graph shows how the speed of a moving object varies with time
  • The red line represents an object with increasing speed
  • The green line represents an object with decreasing speed

Increasing and decreasing speed represented on a speed-time graph

Acceleration on a Speed-Time Graph

• Speed-time graphs also show the following information:
  • If the object is moving with a constant acceleration or deceleration
  • The magnitude of the acceleration or deceleration

• A straight line represents constant acceleration
• The slope of the line represents the magnitude of acceleration
  • A steep slope means large acceleration (or deceleration) - i.e. the object's speed changes very quickly
  • A gentle slope means small acceleration (or deceleration) - i.e. the object's speed changes very gradually
  • A flat line means the acceleration is zero - i.e. the object is moving with a constant speed

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

• The distance travelled by an object can be found by determining the area beneath the graph

 

The distance travelled can be found from the area beneath the graph

 

• If the area beneath the graph forms a triangle (the object is accelerating or decelerating) then the area can be determined using the formula:

 

• If the area beneath the graph is a rectangle (constant velocity) then the area can be determined using the formula:

 

Step 1: Recall that the area under a velocity-time graph represents the distance travelled

• • In order to calculate the total distance travelled, the total area underneath the line must be determined

Step 2: Identify each enclosed area

• • In this example, there are five enclosed areas under the line
  • These can be labelled as areas 1, 2, 3, 4 and 5, as shown in the image below:

  

Step 3: Calculate the area of each enclosed shape under the line

• • Area 1 = area of a triangle = ½ × base × height = ½ × 40 × 17.5 = 350 m
  • Area 2 = area of a rectangle = base × height = 30 × 17.5 = 525 m
  • Area 3 = area of a triangle = ½ × base × height = ½ × 20 × 7.5 = 75 m
  • Area 4 = area of a rectangle = base × height = 20 × 17.5 = 350 m
  • Area 5 = area of a triangle = ½ × base × height = ½ × 70 × 25 = 875 m

Step 4: Calculate the total distance travelled by finding the total area under the line

• • Add up each of the five areas enclosed:

total distance = 350 + 525 + 75 + 350 + 875

total distance = 2175 m