Displacement-time graph

• A displacement-time graph is a graph which shows:
  • the displacement travelled by an object on the y-axis
  • the time on the x-axis.
• They tell us how far away from its starting position an object has travelled over a period of time.

Finding the displacement

• If we want to find the displacmenet from the starting point at a specific time, we can read it off the graph:
  • Find the time on the x-axis.
  • Move vertically up to the line on the graph.
  • Move horizontally to the y-axis to read off the displacement.

Find the displacement of the object at 4 seconds

(displacement, $m$)
24 |                         /
   |                       /
20 |                     /
   |                   /
16 |                 / 
   |               /
12 |             /
   |           /
 8 |         /
   |       /
 4 |     /
   |   /
 0 | /
   |________________________________
     0  1  2  3  4  5  6  7  8  9 10  (time, $s$)

Read off the graph at 4 seconds:

(displacement, $m$)
24 |                         /
   |                       /
20 |                     /
   |                   /
16 |                 / 
   |               /
12 |-------------/
   |           / |
 8 |         /   |
   |       /     |
 4 |     /       |
   |   /         |
 0 | /           |
   |_____________|__________________
     0  1  2  3  4  5  6  7  8  9 10  (time, $s$)

At 4 seconds, the displacement is 12 m.

Answer: 12m.

Finding the velocity

To find the velocity of an object from a displacement-time graph, we need to find the gradient at that point.

If the displacement-time graph is a straight line, the velocity is constant, and we can find the gradient of the line using m=\frac{\Delta y}{\Delta x} - the change in y divided by the change in x.

If it’s not a straight line, we can draw a tangent to the curve at the point we want to find the velocity, and then find the gradient of that tangent line.

Finding the average velocity

To find the average velocity over a period of time, we can use the formula:

\text{average velocity} = \frac{\text{total displacement}}{\text{total time}}

For example, to find the average velocity between 2 seconds and 6 seconds:

• Assume the displacement at 2 seconds is 8 m, and at 6 seconds is 20 m.
• Total displacement = 20m - 8m = 12m
• Total time = 6s - 2s = 4s
• Average velocity = \frac{12m}{4s} = 3m/s