• The area under a?velocity-time graph?represents the?displacement?(or?distance travelled) by an object

The displacement, or distance travelled, is represented by the area beneath the graph

• If the area beneath the graph forms a?triangle?(i.e. the object is?accelerating?or?decelerating), then the area can be determined by using the following formula:

Area = ? × Base × Height

• If the area beneath the graph forms a?rectangle?(i.e. the object is moving at a?constant velocity), then the area can be determined by using the following formula:

Area = Base × Height

Determining Distance from a Velocity-Time Graph

• Enclosed?areas under velocity-time graphs represent?total displacement?(or?total distance travelled)

Three enclosed areas (two triangles and one rectangle) under this velocity-time graph represents the total distance travelled

• If an object moves with?constant acceleration, its velocity-time graph will comprise of?straight lines
  • In this case, calculate the distance travelled by working out the?area?of?enclosed rectangles and triangles?as in the image above

   

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

轉載自savemyexam