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Acceleration v's Time Graph

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3.11Acceleration v's Time Graph


In these revision notes for Acceleration v's Time Graph, we cover the following key points:

  • The meaning of the acceleration vs time graph
  • How to plot the acceleration vs time graph in uniform motion
  • How to plot the acceleration vs time graph for uniformly accelerated (decelerated) motion
  • How to make use of the average acceleration concept in situations involving motions with variable acceleration
  • The relationship between motion graphs and kinematic quantities

Acceleration v's Time Graph Revision Notes

In Uniform Motion, there is no acceleration (a = 0) as the velocity is constant. Therefore, the acceleration vs time graph will be a straight line extending on the horizontal (time) axis.

In the uniformly accelerated (decelerated) motion, the acceleration is constant but not zero. Therefore, it will not be at the horizontal axis but above or below it depending on the sign of acceleration, although it is still horizontal. This means when the acceleration is positive (the object is speeding up), the acceleration vs time graph will be a horizontal line above the time axis and when it is negative (while slowing down), the acceleration vs time graph will be a horizontal line below the time axis.

Acceleration cannot be a scalar; it is always a vector quantity as it can also be negative.

When acceleration changes uniformly, we can make use of the average acceleration concept and then consider the process as a motion with constant acceleration. In this way, we can still use the kinematic formulae (which in fact are valid only for the motion with constant acceleration).

When the motion is irregular, we divide the graph in small sections in which the acceleration is regarded as changing uniformly. Then, the average acceleration concept for each section is used to substitute the values of the irregular acceleration in the given interval.

The following rules express the relationship between kinematic quantities involved in the graphs of motion:

  1. The gradient of the position vs time graph gives the velocity
  2. The gradient of the velocity vs time graph gives the acceleration
  3. The area under (above when negative) the velocity vs time graph gives the change in position (displacement)
  4. The area under (above when negative) the acceleration vs time graph gives the change in velocity

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  2. Kinematics Physics tutorial: Acceleration v's Time Graph. Read the Acceleration v's Time Graph physics tutorial and build your physics knowledge of Kinematics
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  5. Continuing learning kinematics - read our next physics tutorial: Motion in Two Dimensions. Projectile Motion

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