Velocity-time graphs

Determining acceleration

If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the acceleration of the object.

A velocity/time graph. Graph with four distinct sections. All lines are straight.A velocity-time graph

The table shows what each section of the graph represents:

Section of graphGradientVelocityAcceleration
APositiveIncreasingPositive
BZeroConstantZero
CNegativeDecreasingNegative
D (v = 0)ZeroStationary (at rest)Zero
Question

Calculate the acceleration of the object represented by the steepest line in the graph.

A distance time graph shows distance travelled measured by time.

change in velocity = (10 − 0) = 10 m/s

change in time = (2 − 0) = 2 s

acceleration = \frac{change\ in\ velocity}{time}

acceleration = 10 ÷ 2

\underline{acceleration = 5~m/s^{2}}

Calculating displacement - Higher

curriculum-key-fact
The displacement of an object can be calculated from the area under a velocity-time graph. The area under the graph can be calculated by:
  • using geometry (if the lines are straight)
  • counting the squares beneath the line (particularly if the lines are curved)

Example

Calculate the total displacement of the object - its motion is represented by the velocity-time graph below.

The y axis shows velocity in metres per second and the x axis time in seconds.  The object increases its velocity from 0 metres per second to 8 metres per second in 4 seconds.The y-axis shows velocity in metres per second and the x-axis time in seconds. The object increases its velocity from 0 metres per second to 8 metres per second in 4 seconds

Here, the displacement can be found by calculating the total area of the shaded sections below the line.

  1. Find the area of the triangle:
    • \frac{1}{2}\times base \times height
    • \frac{1}{2}\times 4 \times 8 = 16~m^{2}
  2. Find the area of the rectangle:
    • base \times height
    • (10 - 4) \times 8 = 48~m^{2}
  3. Add the areas together to find the total displacement: \underline{(16 + 48) = 64~m}