How to Read Distance-Time Graphs
Distance-Time Graphs are very easy to understand. The X-axis represents the time (secs) and the Y-axis represents the distance. Below is an example of a distance-time graph:
The graph has been split into 5 sections. By doing this, we can explain what the different parts mean.
If you get confused with the descriptions at any point, imagine the object to be a car :)
A: Straight + Positive Correlation = STEADY SPEED
As you can see, the line is directly proportional. This shows us that it is going at a constant speed as the distance steadily increases in accordance to the time. The fact that the line is a positive correlation also tells us that the object that the graph describes is travelling forward; away from the original point (as the Y-axis, distance, represents the distance away from the original point. This is an advantage of distance-time graphs in comparison to velocity-time graphs: they can tell us in which direction the object is going :) Easy!
B: Under-curve + Positive Correlation = ACCELERATING
This line is positive which, just like line A, tells us that the object is travelling forward. It is however curved. Unlike, line A, it is not directly proportional meaning that it is not a steady speed. Alternatively, if we break the line up further, we can see that it first of all travels slower.. but then the *gradient gets steeper and it travels faster! It accelerates!
C: Over-curve + Positive Correlation = DECELERATING
This is just the opposite to line B. (Deceleration is the opposite to acceleration.) Again, if we break the line up, at first, it is steeper, but then it smooths out.. this tells as that the object is slowing down; decelerating.
D: Straight + Flat = STATIONARY
If the line is flat, this means that the object is stationary. This is because in any amount of time, the car has not traveled any distance; it hasn't moved.
E: Straight + Negative Correlation = STEADY SPEED
This is similar to line A. Just like line A, this is straight, and so is directly proportional and travels at a steady speed. However, the distance seems to decrease. As we have established, the Y-axis, distance, describes the distance away from the original starting point.. So this means that the object is going back to that point; the distance away from that object is decreasing. ^o^
*Gradient = The line's gradient is its height ÷ length
How to Find the Speed
The distance-time graphs tells us 2 different pieces of information: the DISTANCE and TIME (surprisingly xD).
Does that remind you of something?
Of course. The distance-speed-time formula triangle!
You can work out the speed that the object is travelling by dividing the distance by the time; finding the gradient.
Eg: Find the speed that the object travels at during the last 20 seconds.
(using the graph at the top of the page)
Using the triangle, find the values that you need and number crunch.
Distance traveled: -60m (as it is a negative correlation)
Time: 20secs (given in the question 90-70secs)
And so... -60÷20=-3m/s
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