=Distance -Time Graphs= ''''Distance'''' is the total length travelled by an object. The standard unit is the ''''metre''''. A distance-time graph shows how far an object has travelled in a given time. Distance is plotted on the Y-axis (left) and Time is plotted on the X-axis (bottom). Below you can see that the object represented by the blue line has travelled 10m in 2s whereas the object represented by the red line has only travelled 4m in this time and is therefore travelling more slowly. [image://i.imgur.com/qKjSSIo.png] ''''Straight lines'''' on a distance-time graph tell us that the object is travelling at a '''constant speed'''. Note that you can think of a stationary object (not moving) as travelling at a constant speed of 0 m/s. On a distance-time graph, there are no line sloping downwards. A moving object is always ''''increasing'''' its total length moved with time. [image://i.imgur.com/m72vOWp.png?1] ''''Curved lines'''' on a distance time graph indicate that the speed is changing. The object is either getting faster = ''''accelerating'''' or slowing down = ''''decelerating''''. You can see that the distanced moved through each second is changing. ==Calculating Speed from a Distance-Time Graph== [image://i.imgur.com/SZupBpn.png?1] The average speed can be calculated for any part of a journey by taking the change in '''distance''' and dividing by the change in '''time''' for that part of the journey. You can even do this for a curved line where the speed is changing, just remember that your result is the '''average''' speed in this case. You may also notice that the formula for calculating speed is sometime written with small triangles '''Δ''' (the Greek letter delta) in front of '''d''' (distance) and '''t''' (time). The '''Δ''' is just short hand for '''"change in"'''. Therefore '''Δt''' means '''"change in time"''' [image://i.imgur.com/ULJd8Ds.png] ==Displacement== ''''Displacement'''' is the length between start and stop positions and includes a direction. Displacement is a vector quantity. [image://ocw.uci.edu/cat/media/OC08/11004/OC0811004_L6Graphic06.gif]If an object goes back to where is started in certain time, then its displacement is zero. Its distance would be the total length of the journey. A displacement-time graph is able to show if an object is going backwards or forwards. Usually, a line with a negative gradient would indicate motion going backwards. This cannot be shown on a distance-time graph. Image Source: //ocw.uci.edu/ ==Describing the motion of an object== In most mechanical problems we are asked to determine the connection between speed, position and time. Will two cars crash if they are heading towards each other as they apply brakes at a certain time? To describe the position of a moving object, you have to specify its position relative to a particular point or landmark that is understood by everyone. Along a straight line, you only need the position of the landmark and how far the object is from the landmark left or right (or east or west). 5 metres from the door does not mean anything without giving some indication of direction (inside or out for example). Now left or right is not a good distinction as not everyone can agree with it. In Physics, we specify the origin landmark at 0 and the points either side of it are either positive or negative numbers (in units of metres). [image://i.imgur.com/CGRPorR.png] When describing the motion of an object try to be as detailed as possible. For instance... During ''''Part A'''' of the journey the object travels '''+8m''' in '''4s'''. It is travelling at a '''constant velocity''' of '''+2ms^-1^''' During ''''Part B'''' of the journey the object travels '''0m''' in '''3s'''. It is '''stationary for 3 seconds''' During ''''Part C'''' of the journey the object travels '''-8m''' in '''3s'''. It is travelling at a ''''constant velocity'''' of ''''-2.7ms^-1^'''' back to its starting point, our reference point 0. Why can we use ''''velocity'''' instead of ''''speed''''? Because by labelling our two directions + and -, we now know which way our object is moving in 1-dimension, forwards or backwards.
Calculating the speed from a distance-time graph
To find the speed of an object from a distance-time graph, we need to calculate the gradient (or slope) of the line.
First choose two points that lie the line - say point A is (0 , 0) and point B is (10 , 50). These are quite far apart so that will make our gradient calculation more accurate.
Now draw a right-angled triangle with two horizontal and vertical sides. Starting at point A, we move 10 seconds along the base of the triangle, so the 'run' is +10 secs.
Now move up the vertical side of the triangle a distance of 50 metres. This is our 'rise' = +50m
Use the formula: Gradient = Rise/Run and sub-in the numbers
= 50/10
= 5
The speed shown in this distance time graph is therefore 5 m/s.
(Note that you could also have used the formula: Average Speed = Distance travelled / Time taken
This would have given us the same result.)
GCSE Physics Keywords: Gradient, Rise, Run, Distance, Time, Speed
Course overview
How can we determine the speed of an object from its distance time graph
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