Reading Kinematics Graphs

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Distance-Time Graphs

distance time graph
  • For a distance-time graph, the distance never decreases.
  • When the object is stationary, the distance-time graph will be horizontal.
  • The gradient of a distance-time graph is the instantaneous speed of the object.
  • For straight line with positive gradient, it means that the object is travelling at uniform speed
  • There is no straight line with negative gradient (as the distance never decreases)
  • For curves, it means that the object is travelling at non-uniform speed

Displacement-Time Graphs

  • The details are similar as distance-time graphs, except that the distance is now displacement, and speed is now velocity.
  • One minor difference: There is a straight line with negative gradient, it means that the object is travelling at uniform velocity in the opposite direction.

Velocity-Time Graphs

velocity-time graph
  • When the object is stationary, it is a straight horizontal line at 0.
  • When the object is undergoing uniform motion, it is a straight horizontal line at $v \, \text{m s}^{-1}$, where v is the velocity of the object.
  • For straight line with positive gradient, it means that the object is accelerating.
  • For straight line with negative gradient, it means that the object is decelerating.
  • For curves, it means that the acceleration of the object is changing.
  • The area under the graph is the change in the displacement of the object.

Acceleration-Time Graphs

  • Area under graph is the change in the velocity of the object

Summary of Kinematics Graphs

The figure below shows the displacement-time graph, velocity-time graph and acceleration-time graph for the respective state of motion. It serves as a summary of the text above.

all graphs of motion

The figure below shows the relationship between displacement-time graph, velocity-time graph and acceleration-time graph.


Self-Test Questions

Can you tell from a displacement-time graph whether an object is stationary?

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Yes. If the object is stationary, it will appear as a horizontal line on a displacement-time graph.


How can you obtain the average velocity and instantaneous velocity from a displacement-time graph.

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The average velocity can be found by using $\frac{\text{total displacement}}{\text{total time taken}}$.

The instantaneous velocity at a point in time can be found from the gradient of the tangent to that point in time.


Can you tell from a velocity-time graph whether an object is stationary?

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Yes. If the object is stationary, the velocity-time graph will be a horizontal line at $\text{v}=0$.


How would you obtain the acceleration of an object from a velocity-time graph? What does the area under a velocity-time graph represent?

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The acceleration of an object at a point in time can be obtained from the gradient of the tangent to that point in time.

The area under a velocity-time graph represents the total distance traveled.


Can you tell from an acceleration-time graph whether an object is stationary?

Show/Hide Answers

No, you cannot. Do you know why?

Hint: Refer to the summary of Kinematics graphs (located above).

Drop a comment below if you cannot figure out the answer.


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20 thoughts on “Reading Kinematics Graphs”

  1. For those finding the answe, look below: stationary object means 0 velocity hence velocity donot changes so acc=0 (acc is the rate at which velocity changes). Now acceleration is also 0 when object moves with constant velocity.. as a result we cannot predict whether or not object is stationary from acceleration time graph.

    Reply
  2. Can you tell from an acceleration-time graph whether an object is stationary?

    No, you cannot. Do you know why?

    Drop a comment below if you cannot figure out the answer.
    I would like to know the answer!

    Reply
    • area under graph for the acceleration time graph gives u the ‘Change’ in velocity. when an object is stationary , it has zero velocity. Stationary objects wont have any acceleration either as they r not moving thus don,t have any velocity and acceleration basically is the rate of change of velocity. hope this helped

      Reply
    • Because acceleration 0 does not say that velocity is 0 , though the object does not have force but it can be yet in motion.

      Reply

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