Area under a Velocity-Time Graph (CIE A Level Physics)

The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.

Calculate the displacement of the vehicle at 40 s.

Answer:

Step 1: State how to determine the displacement

• The displacement is equal to the area under a velocity-time graph

Step 2: Determine the scale on the graph

• Each division is

Step 3: Determine the base and height of the graph

• Time = base = 40 s
• Velocity = height = 105 km h^–1

Step 4: Convert km h^-1 into km s^–1

$\frac{105}{60 \times 60} = 0.0292 \mathrm{km} {\mathrm{s}}^{-1}$

Step 5: Calculate the area under the graph

 Area of a right-angled triangle =  $\frac{1}{2} \times base \times height$

$Area =\frac{1}{2} \times 40 \times 0.0292 = 0.6 \mathrm{km}$