Forces: Velocity-Time Graphs

Forces: Velocity-Time Graphs

Understanding Velocity-Time Graphs:

  • A velocity-time graph represents the velocity of an object against time.
  • Time is usually on the x-axis and velocity on the y-axis.
  • The gradient of a velocity-time graph shows the acceleration of the object. Steeper gradient means a higher acceleration. A horizontal line indicates constant velocity.
  • A negative gradient shows deceleration or slowing down.

Calculating Distance:

  • The area under the graph between the time axis (x-axis) and the graph line represents the distance travelled by the object.
  • The total area under the line can be calculated by dividing it into appropriate shapes such as rectangles or triangles, calculating the area of each shape and adding these areas together.
  • While calculating the distance, remember that the area of a rectangle is given by base x height and the area of a triangle is given by 1/2 x base x height.


  • Acceleration is the rate at which velocity changes with time.
  • Acceleration is calculated using the formula: acceleration = change in velocity / time taken.
  • It can be determined from a velocity-time graph by finding the gradient of the graph.
  • If a graph line slants upwards, the object is accelerating. If it slants downwards, it’s decelerating.
  • Acceleration due to gravity is a special case and is approximately 9.8 m/s² downwards.

Deceleration and Negative Acceleration:

  • Deceleration or negative acceleration refers to reducing speed i.e., the object is slowing down.
  • On a velocity-time graph, deceleration is represented by a line sloping downwards.

Understanding Stationary Objects:

  • A horizontal line on the graph (where gradient = 0) shows that the object is moving at a constant velocity, or it may be stationary. If the line is along the x-axis (velocity = 0), the object is stationary.