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2.3.1 Displacement-Time Graph

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  1. There are 3 types of motion graph, namely
    1. the displacement-time graph
    2. the velocity-time graph
    3. the acceleration-time graph.
  2. When analysing a graph, it's important for us to know what's the physical quantity that's represented by the gradient of the graph and the area below the graph. 
  3. For example, in a displacement-time graph, the gradient represent the velocity of the moving object, whereas in a velocity-time graph, the gradient represent the acceleration of the moving object.
  4. It's also important for you to know how to find the gradient of a straight line from a graph.
  5. Sometime, you will be asked to convert a displacement-time graph to a velocity-time graph or convert a velocity-time graph to an acceleration-time graph.

Displacement - Time Graph



In a Displacement-Time Graph, the gradient of the graph is equal to the velocity of motion.

Analysing Displacement - Time Graph

  1. When analysing displacement-time graph, always remember that the gradient of the graph represents the velocity of the graph.
  2. Therefore, if the gradient of the graph is positive, the velocity is positive, and if the gradient of the graph is negative, the velocity is negative.
  3. A negative velocity indicates that the object moves in opposite direction.
  4. Table below shows the displacement-time graph of various motion.


Velocity = 0
This is a horizontal straight line, hence the gradient = 0.
Therefore, the velocity = gradient of the graph = 0, which means the object is stationary (does not move).


Uniform Velocity

The graph is a non-horizontal straight line, hence the gradient is not equal to 0. For a straight line, the gradient is constant, hence, the velocity of the moving object is uniform.

Negative Uniform Velocity
The graph is a non-horizontal straight line, with negative gradient. For straight line, the gradient must be constant. The negative value of gradient indicates that the object moves in opposite direction.
Therefore, this graph represents a motion with uniform velocity in opposite direction.

Increasing Velocity
The graph is a curve, shows that the gradient is not constant. The gradient increases over time, indicates that the velocity increases over time.

Decreasing Acceleration
The gradient decreases over time, shows that the velocity of the moving object decreases over time.