Warm Up – February 1, 2016.

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Presentation transcript:

Warm Up – February 1, 2016

UNDERSTANDING AND INTERPRETING DISTANCE-TIME GRAPHS

DISTANCE – TIME GRAPHS Plotting distance against time can tell you a lot about a journey. Let's look at the axes: Time always runs horizontally (the x-axis). The arrow shows the direction of time. The further to the right, the longer time from the start. Distance runs vertically (the y-axis). The higher up the graph we go, the further we are from the start.

NOT MOVING… If something is not moving, a horizontal line is drawn on a distance-time graph (D/T-graph). Time is increasing to the right, but its distance does not change. It is stationary.

MOVING… If something is moving at a steady speed, it means we expect the same increase in distance in a given time: Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

STEADY SPEED… If something is moving at a steady speed, it means we expect the same increase in distance in a given time: Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

Can you describe what is happening here? For the first part of the journey shown by the graph below, the object moved at a steady (slow) speed. It then suddenly increased its speed, covering a much larger distance in the same time. This sort of motion is not very realistic, but is easy to understand. It also makes calculations easier!

What is the effect of line ‘Steepness’, A.K.A slope… Both the lines below show that each object moved the same distance, but the steeper line got there before the other one: A steeper slope indicates a larger distance moved in a given time. In other words, higher speed. Both lines are of constant gradient, so both speeds are constant.

ACCELERATION… The line below is curving upwards. This shows an increase in speed, since the slope is getting steeper: In other words, in a given time, the distance the object moves is larger. It is accelerating.

What is happening here? Moving at a steady speed, slowly Not moving for quite some time Moving again, but at higher speed In all the graphs so far, we have not seen any numbers - it's about time we did!

Calculating Speed from D/T Graph We can see that the motion shown by the steeper line is fastest. By definition, speed = distance / time so the steepness (or slope) of the line will give us the speed! Line A: speed = distance / time = 40 m / 10 s = 4 m/s Line B: speed = distance / time = 20 m / 20 s = 1 m/s

Calculating speed from different sections of a D/T Graph. Part A: speed = distance / time = 100 m / 10 s = 10 m/s Part B: speed = distance / time = 50 m / 10 s = 5 m/s Part C: speed = distance / time = 150 m / 20 s = 7·5 m/s What is the AVERAGE SPEED OF THE TRIP?