1. Velocity/time graphs The first thing to note about these is that, on first glance, they look EXACTLY the same as distance time graphs! distance time graphs

2. Can you spot the difference? The only way you can tell the difference is by reading the labels on the axes. HINT: Always read the labels on the axes! Failure to do so can mean you completely mis-interpret what it shows.

3. Just like distance/time graphs, there are some basic graphs to learn. The first is just a horizontal line: Don't be tempted to think this means it's stationary! This is speed/time, and the speed is both positive and constant. This shows a constant speed.

4. The speed is increasing, so the object must be accelerating.

5. The speed is decreasing, so the object must be decelerating. Note that this shape of distance-time graph would mean steady speed back to where you came from. Totally different!

6. Both the yellow and blue line show increasing speed. They both reach the same top speed, but the blue one takes longer. What is the difference? The yellow line shows a greater acceleration.

7. Speed-Time graphs can be used to find out how far something has travelled. In the example below, a speed of 30 m/s is maintained for 20 seconds: One way of calculating the distance is to use distance = speed × time. This gives: distance = 30 × 20 = 600 m

8. An alternative way of finding the distance travelled is simply to calculate the area under the line: In this case: distance = 30 × 20 = 600 m. Which is precisely the same calculation as before!

9. The average speed can be used to find the distance travelled: Average speed = (10 + 30) / 2 = 20 m/s Distance = average speed × time Distance = 20 × 20 = 400 m

10. Alternatively, the area may be found underneath the line: Blue rectangle = 20 × 10 = 200 m White triangle = (20 × 20) / 2 = 200 m Total distance = 200 + 200 = 400 m

11. You will already have learned about acceleration. Speed-time graphs can also be used to find accelerations:acceleration The purple line shows an acceleration from 0 to 30 m/s in 20 seconds. The blue line shows an acceleration from 0 to 20 m/s in 20 seconds.

12. The gradient of the purple line is (30-0) / 20 = 1.5 m/s/s. The gradient of the blue line is (20-0) / 20 = 1 m/s/s.

13. Look at the graph. Find the accelerations shown by the green and red lines. Also calculate the deceleration shown by the blue line. Finally find the total distance travelled.

14. The green line shows an acceleration of 1 m/s/s The red line shows an acceleration of 2 m/s/s The blue line shows a deceleration of 3 m/s/s. Finally the total distance travelled is: 50 + 200 + 150 = 400 m