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=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:http://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:https://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:http://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:http://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:http://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: http://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:http://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.
A distance-time graph shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Note: Curved lines on a distance-time graph indicate that the speed is changing. You may also want to check out these topics given below! We deal with the distance-time graph while studying the motion of bodies. If we record distance and time for the motion of a body and plot the same data on a rectangular graph, we will obtain a distance-time graph corresponding to the motion of that body. For better understanding, let us consider an example of uniform motion. A bus driver drives at a constant speed which is indicated by the speedometer and the driver measures the time taken by the bus for every kilometre. The driver notices that the bus travels 1 kilometre every 2 minutes. Data Table He prepares the data table after this so that he has a clear understanding of everything and then draws the graph as shown below. By this table, he had a clear idea about the speed which is: ½ × 60 = 30 km/hr. The graph is a straight line and the motion of the bus is also uniform. Also, from the graph, we can find the speed of the bus at any instant of time. The initial and final position of the car can be found as the following: Speed = (Final Position-Initial position)/Time The slope of the line can be found by drawing a rectangle anywhere near the straight line which determines the speed of the bus. If an object is not moving, the distance-time graph results in a horizontal line which shows that the object is at rest.  Conclusion:The following things can be concluded now:
What is Velocity -Time Graph and Displacement-Time Graph?
A graph is defined as a pictorial representation of information which is a two-dimensional drawing showing the relationship between dependent and independent variables. Independent variables are denoted on the horizontal line known as the x-axis, while the dependent variables are denoted on the vertical line known as the y-axis. The main components of a 2D graph are x-coordinate and y-coordinate. Displacement time graph, velocity-time graph, and acceleration time graph are three common types of graphs in classical mechanics. In the distance-time graph, distance is the dependent variable and is represented on the y-axis, while time is the independent variable and is represented on the x-axis. The slope of the distance-time graph represents the speed of an object.
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What are the characteristics of distance time graph for an object moving at a uniform speed?
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