5.11 - Velocity-Time Graphs

Reading a velocity-time graph

A velocity-time graph shows how an object's velocity changes as time passes.

• A flat section means a steady (constant) velocity.
• An uphill section (going up to the right) means the object is accelerating.
• A downhill section (going down to the right) means the object is decelerating.
• The steeper the line, the greater the acceleration or deceleration.
• A straight line means constant acceleration.
• A curve means the acceleration is changing.

The gradient gives the acceleration

• The gradient (steepness) of a velocity-time graph equals the object's acceleration - it's the change in velocity divided by the time taken.
• For a straight section, divide the change in velocity (the rise) by the time taken (the run).

Finding the acceleration on a curve

• Where the line is curved, the gradient is different at every point.
• To find the acceleration at a particular moment, draw a tangent to the curve at that point and find the gradient of the tangent.

A line below the time axis

• If the line drops below the time axis, the object has a negative velocity.
• This means it's moving in the opposite direction.

Worked example - Acceleration from a velocity-time graph

A velocity-time graph shows a car's journey. The velocity rises in a straight line from 0 to 24 m/s over the first 8 s, then stays constant at 24 m/s. Find the acceleration of the car over the first 8 s.

The acceleration is the gradient of the line over the first 8 s.