2.3.2 Velocity – Time Graph

Analysing Velocity-Time Graph

1. When analysing velocity-time graph, always keep in mind that the gradient of the graph is equal to the acceleration of the graph.
2. If the gradient is constant, then the acceleration is constant. If the gradient increase, then the acceleration increase and etc.
3. Table below shows a few cases of velocity-time graph for different types of motion.

Uniform velocity

Uniform acceleration

Increasing acceleration

Uniform deceleration

Decreasing acceleration

Converting a Velocity-Time graph to Acceleration-Time graph

1. In order to convert a velocity-time graph to acceleration time graph, we need to find the gradient of the velocity time graph and plot it in the acceleration-time graph.
2. The 5th and 6th videos below explain how to sketch an acceleration-time graph form a given velocity-time graph.

Free Falling

1. Free falling is a motion under gravitational force as the only force acting on the moving object.
2. The acceleration of a free falling object is always constant.
3. On the surface of the earth, the acceleration of is equal to 10ms^-2, and is named as gravitational acceleration.
4. In SPM, you need to know the graphs of free falling of the following movement
   1. Launching object upward.
   2. Dropping Object from High Place
   3. Object Falling and Bounce Back

Launching Object Upward

1. When you launch an object upward, its velocity decreases at a constant rate, hence it's a straight line with negative gradient in a velocity-time graph. 
2. Since the velocity decreases at a constant rate, hence the acceleration is constant. Also, the acceleration is negative because the speed decreases in positive direction. Therefore, the acceleration graph is a horizontal line in the negative domain.

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1. When an object drops from a high place, its velocity increases at a constant rate, hence it's a straight line with positive gradient in a velocity-time graph. 
2. Since the velocity increases at a constant rate and the speed increases in positive direction hence the acceleration is constant and positive.