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This is a tricky concept that nails a lot of kids on the first few physics tests. Lets say your sitting at home on a Saturday nite with nothing to do. Suddenly the phone rings, it's that new girl from France. She says she desperately needs you to help with her pronunciation of English words. You travel to her house, (5 blocks away) help her to position her tongue correctly and then return home. "What was the distance you traveled?" I ask "10 blocks" you say. Very good. That's the easy one. Displacement is harder. Displacement is the distance between where you start the trip and where you end the trip. In this example your displacement would be zero. This is because you start and stop at the same place, your house.
Here is another example. If you walked five blocks to the French girl's house and stayed there, your distance and displacement would be the same, 5 blocks. However if you were to walk to her house, stay a while and walk three blocks back before being gunned down by a rival gang, the distance you traveled would be 8 blocks and your displacement would be 2 blocks. You walked 8 blocks, that is the distance, but it is only two blocks from your house (the starting place of the trip) to where the poliece will find your bullet riddled body (the unintended ending place of the trip)
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Displacement is also a vector quantity. The direction points from the start of the trip to the end of the trip. |
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| The symbol for displacement is a lowercase 's' |
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Velocity, like displacement is a vector. Velocity, or more technically, average velocity, is defined as the displacement, over how long it took for that displacement to occur, the time.
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Where does the direction of the velocity come from? It is the same as the direction of the displacement. This only makes sense if you think about it. If you run 20m west in 5 seconds, your velocity, 4m/s, would have to be west.
As a side note, a lot of times we just use + and - to indicate direction, so don't expect every vector to have a direction after it, like north or 10° South of West.
As we said in the last section v=s/t will give us the average velocity. When we find the average of something it usually means that there is a difference in the values at the beginning and at the end. Lets say your driving your car down the street at a calm 20m/s. Way off in the distance you see a mime pretending to be trapped in a box. You hate mimes. Being the responsible citizen that you are, you floor it and aim straight for the mime. The car leaps forward and the mime quickly panics and tries to escape from his self made prison. Alas, it is no use, the invisible walls prove too strong for him. Your car, firmly grounded in reality, passes right through the nonexistent box and hits the mime at a smooth 120m/s. He goes flying down the street, cracks open his skull with a satisfying thud, and squirrels eat him. The point of this story, besides expressing my hatred of mimes, was to show that there was a change in velocity. From 20m/s to 120m/s. Acceleration describes how quickly velocity changes.
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| Its all the same. The little triangle is the Greek letter delta, yes, just like the airline. Delta means 'change in'. To find the change in something, just subtract the initial value from the final value. Now lets find your acceleration in the previous paragraph. Assume that you went from 20m/s to 120m/s in 25 seconds. |  |
m/s2 What the hell is that? m/s2 is the mathematical shortcut way of saying meters per second per second. Still not helping? Ok, meters per second we understand. You travel 4 meters for every one second of time that passes. Now 4m/s2 means that for every second that passes you will be going 4m/s faster than you were before. An increase in speed of 4 m/s per second. 4m/s/s or 4m/s2
By using v=s/t and a=(vf - vi)/t we can get all the equations we need for one dimensional kinematics, these are.
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The velocity (average) is equal to the displacement traveled over the time it took to travel that displacement.
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The acceleration (average) is equal to the change in velocity (final minus initial) over the time it took for that change to occur.
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The final velocity is equal to the initial velocity plus the acceleration multiplied by the elapsed time.
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The displacement is equal to half the (final velocity plus the initial velocity) multiplied by the time.
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The final velocity squared is equal to the initial velocity squared plus twice the acceleration multiplied by the displacement .
If any of the above was unclear, or if you have any comments or suggestions, please E-mail me!
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