Distance-time graph

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

Finding the distance

• If we want to find the distance travelled 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 distance.

Find the distance travelled by the object at 4 seconds

(distance, $m$)
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:

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

At 4 seconds, the distance is 12 m.

Answer: 12m.

Finding the speed / velocity

To find the speed (or velocity) of an object from a distance-time graph, we need to find the gradient at that point.

If the distance-time graph is a straight line, the speed 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 speed, and then find the gradient of that tangent line.

Finding the average speed

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

\text{average speed} = \frac{\text{total distance}}{\text{total time}}

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

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