Area under a Velocity-Time Graph (Edexcel IGCSE Science (Double Award): Physics): Revision Note

The velocity-time graph below shows a car journey that lasts for 160 seconds.

Calculate the total distance travelled by the car.

Answer:

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

$A_1=\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

$A_1=\frac{1}{2}\times 40\times 17.5$

$A_1=350\mathrm{m}$

• Area 2 = area of a rectangle

$A_2=\mathrm{base}\times \mathrm{height}$

$A_2=30\times 17.5$

$A_2=525\mathrm{m}$

• Area 3 = area of a triangle

$A_3=\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

$A_3=\frac{1}{2}\times 20\times 7.5$

$A_3=75\mathrm{m}$

• Area 4 = area of a rectangle

$A_4=\mathrm{base}\times \mathrm{height}$

$A_4=20\times 17.5$

$A_4=350\mathrm{m}$

• Area 5 = area of a triangle

$A_5=\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

$A_5=\frac{1}{2}\times 70\times 25$

$A_5=875\mathrm{m}$

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

• Add up each of the five areas enclosed:

$\mathrm{total}\mathrm{distance}=A_1+A_2+A_3+A_4+A_5$

$\mathrm{total}\mathrm{distance}=350+525+75+350+875$

$\mathrm{total}\mathrm{distance}=2175\mathrm{m}$

Some areas will need to be split into a triangle and a rectangle to determine the area for a specific time interval, like areas 3 & 4 in the worked example above.

If you are asked to find the distance travelled for a specific time interval, then you just need to find the area of the section above that time interval.

For example, the distance travelled between 70 s and 90 s is the sum of Area 3 + Area 4.

If the velocity-time graph has a curved line, you can estimate the area under the curve by dividing it into multiple triangles and rectangles similar to the worked example above.