## Distance-Time Graphs

- 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

- 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.

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?

**Show/Hide Answers**

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.

**Show/Hide Answers**

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?

**Show/Hide Answers**

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?

**Show/Hide Answers**

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.

which curve are they taking in distance time graph , either the accelerating one or the slowing down curve ?

I can’t figure out why an object can’t be stationary in the acceleration time graph.

This is because both stationary and constant speed are represented in the same way on an acceleration time graph so you won’t really be able confirm whether it is constant speed or acceleration simply by looking at the graph

Because in the acceleration time graph, both the uniform motion and the sationary object have the same horizontal line at a= 0 m/s2. (Metres per second square)

Thus, you won’t be bale to cnfirm whether the object is stationary or moving at a constant velocity.

This is a helpful and appreciable work but if you could make it more beautifully presented and well illustrated, it would be even better!

i knw in acceleration – time graph an object cannot be in stationary bcoz impulsive makes the object change its momentum by collision which makes einsteins equation falls .

great!

I found it really helpful. Keep up the great work!. Concepts are clear now.

Thank you

Great

Thanks for the website……starting to love physics now. Very useful.

I find physics very hard at school…….but now i glad that i have found this website thank you…..:-)

Helpful!