大象传媒

Velocity-time graphs - Higher

Velocity-time graphs show how the of a moving object changes with time.

What is shown on the velocity-time graph?

A velocity/time graph. Graph with four distinct sections. All lines are straight.
  • Constant is shown by a straight rising line, A.
  • Constant retardation (or deceleration) is shown by a straight falling line, C.
  • Constant velocity is shown by a horizontal line, B.
  • A horizontal line along the X-axis shows the speed is zero, meaning that the vehicle has stopped, or is stationary, D.

The table shows what each section of the graph represents:

Section of graphGradientVelocityAcceleration
APositiveIncreasingPositive
BZeroConstantZero
CNegativeDecreasingNegative
DZeroStationary (at rest, v = 0)Zero
Section of graphA
GradientPositive
VelocityIncreasing
AccelerationPositive
Section of graphB
GradientZero
VelocityConstant
AccelerationZero
Section of graphC
GradientNegative
VelocityDecreasing
AccelerationNegative
Section of graphD
GradientZero
VelocityStationary (at rest, v = 0)
AccelerationZero

The slope or gradient of a velocity-time graph =

\(\frac{\text{final velocity 鈥 initial velocity}}{\text{time taken}}\) = acceleration

Example

Velocity-time graph above is for a racing car accelerating from rest.

The velocity-time graph above is for a racing car accelerating from rest.

Question

What is the acceleration in the first 10 s?

Question

What is the acceleration of the car between 30 s and 50 s?

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