1. Mechanics : Distance v.s. time graphs By the end of this presentation, you should be able to: Plot and sketch distance / time graphs for moving objects. Use these graphs to describe the motion at any time during the object’s journey. Determine the speed (or velocity) of an object from a distance time graph.

2. Use graph paper to plot the distance/ time graph for the car described. 1. At the beginning of the experiment (t=0s) the car is stationary and point X. 2. Once it begins to move it covers 5m in every second for the first 10 seconds of the experiment. 3. It then slows down. It is recorded that the car only covers 30m in the next 10 seconds. 4. The brakes are then suddenly depressed and the car comes to a complete and sudden stop. 5. Plot a distance v.s. time graph for 0 to 30 seconds of time.

3. The graph Distance (m) Time (s) 1020 30 20 40 60 80 X X X X X XX

4. What information can we get from this graph? 1. What is the speed of the car in each of the 10s periods? 2. How far does the car travel in the first 2s of motion? 3. How far does it travel in the next 2s of motion? 4. In which of the 10s periods is the speed constant? 1020 30 20 40 60 80 1a. From 0s to 10s; speed = 50/10 = 5m/s 1b. From 10s to 20s; speed = 30/10 = 3m/s 1c. From 20s to 30s; speed = 0/10 = 0m/s Distance (m) Time (s)

5. What information can we get from this graph? 1020 30 20 40 60 80 Can you see a link between the calculated values of speed and the gradient of the line in each stage? The higher the speed, the steeper the gradient. In fact, the gradient = the speed 5m/s 3m/s 0m/s Distance (m) Time (s)

6. What information can we get from this graph? 2. How far does the car travel in the first 2s of motion? The car travels a total of 5 x 2 = 10m in the first 2s. 3. How far does it travel in the next 2s of motion? The car travels the same distance in the next 2s = 10m 1020 30 20 40 60 80 Distance (m) Time (s)

7. What information can we get from this graph? 1. What is the speed of the car in each of the 10s periods? 2. How far does the car travel in the first 2s of motion? 3. How far does it travel in the next 2s of motion? 4. In which of the 10s periods is the speed constant? 1020 30 20 40 60 80 The car travels at a constant speed of 5m/s in the first 10s, then at a constant speed of 3m/s in the next 10s. The car is stationary in the final 10s. Distance (m) Time (s)

8. DISTANCE /TIME GRAPHS : SUMMARY The gradient = the speed of the object Speed = distance / time (measured in m/s) A straight line means the speed is constant. A constant speed means the distance is changing by the same amount every second. d s x t d : distance covered in metres (m) s : speed or velocity in metres per second (m/s) t : time in seconds (s)

9. Sketching graphs for other objects How do you think the distance time graphs for the following objects will look? 1. A rocket. 2. A parachutist. 3. A wind up toy. 4. A balloon racer. Draw your axes and label them. Then sketch the line or curve as you think is appropriate. d(m) t(s)