Teach A Level Maths Distance and Speed

Volume 4: Mechanics 1 Distance and Speed "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" © Christine Crisp

m s -1 means “metres per second”. It can also be written as m/s. Suppose I move at a steady speed of 1 m s -1 . . . and then I stop for 2 s each time before I move again, so, m s -1 means “metres per second”. It can also be written as m/s. Move Speed (m s -1) Time (s) 2 m right 1 2 at rest 2 m left Since the motion is in a straight line we can show the information on graphs: one for distance-time and one for speed-time.

2 m right 1 2 2 m left Move Speed (m s-1) Time (s) at rest time (s) 2 m left time (s) distance (m) x speed (ms-1) time (s) Working with your partner, copy and complete the sketches.( A version suitable for photocopying is included at the end of this presentation. )

Distance moved can never decrease, so the graph can never come down. Speed (m s-1) Time (s) 2 m right 1 2 at rest 2 m left time (s) distance (m) A straight line shows constant speed. A line parallel to the time axis shows zero speed. I’m at rest. Distance moved can never decrease, so the graph can never come down.

We are illustrating a modelling assumption. Move Speed (m s-1) Time (s) 2 m right 1 2 at rest 2 m left speed (ms-1) time (s) The times I’m at rest are shown by a line along the time axis. The graph shows me moving from a speed of 1 ms-1 to zero in no time. In real life this cannot happen. We are illustrating a modelling assumption.

speed (ms-1) distance (m) Each graph gives us the information on the other. speed (ms-1) time (s) distance (m) x Use the 1st section of each graph to tell your partner how we can get speed from the distance-time graph and distance from the speed-time graph.

2 distance (m) speed (ms-1) 2 2 ÷ 2 = 1 time (s) time (s) 2 Answers: x speed (ms-1) time (s) 2 2 2 ÷ 2 = 1 2 Answers: Constant speed is given by distance divided by time, so it is the gradient of the distance-time graph. Distance is speed  time, so equals the area under the speed-time graph.

On a journey where speed varies, it is useful to refer to average speed. total distance total time e.g. Find the average speed for the 1st eight seconds of the motion shown in the graph. Solution: time (s) distance (m) 4 8 Average speed = = 0·5 m s -1 4 8

SUMMARY Motion in a straight line can be illustrated on graphs. On a distance-time graph, gradient gives speed ( never negative ). speed (ms-1) time (s) 2 time (s) distance (m) 6 2 3 area = 6 gradient = 3 On a speed-time graph, area gives distance.

EXERCISE Use the speed-time graph shown below to sketch a graph of distance travelled against time. speed (ms-1) time (s) What is the total distance travelled ? Your sketch need not use squared paper nor be to scale but you must mark the key values on the axes.

12 + 0 + 4 + 15 = 31 m EXERCISE Solution: speed (ms-1) time (s) distance (m) time (s) 31 10 16 7 15 12 12 3 4 5 Distance = 12 + 0 + 4 + 15 = 31 m

The slides that follow are in a form suitable for photocopying for example 1 and the summary.

Distance and Speed - Data and Graphs for e.g.1 time (s) distance (m) speed (ms-1) 2 1 2 m left at rest 2 m right Move Time (s) Speed (m s-1) Distance and Speed - Data and Graphs for e.g.1

6 3 2 TEACH A LEVEL MATHS – MECHANICS 1 DISTANCE AND SPEED Summary speed (ms-1) time (s) 2 distance (m) 6 Motion in a straight line can be illustrated on graphs. On a distance-time graph, gradient gives speed ( never negative ). On a speed-time graph, area gives distance. 3 gradient = 3 area = 6