Acceleration All Across The Nation
When biking, Dustin knows what his velocity is once he gets started, but he wonders how fast can he get to that point. He knows that when he starts his velocity is 0m/s. He knows that when he gets to a steady speed he likes, his velocity is 20m/s. This takes him 120 seconds. He's starting to understand the physics of biking and so he's pretty sure that he can relate these three numbers so he can figure out at what rate he can get to that point. After he spends many sleepless nights (after he's done all of his homework, of course) trying to figure it out, he asks Mr. Gustafson who informs him to research "acceleration". So Dustin, being the diligent student he is, does just that. He finds out that acceleration is the change in velocity over the change in time.
So if we plug the numbers Dustin all ready knows into the equation, we find that his velocity is
1/6 m/s�. Now that he has the rate figured out, he's very eager to try more problems dealing with rates and the like. Maybe he should find out the rate it takes him to do English Essays!
Once Dustin has finished all of his English Essays, he decides to take a victory lap down the street on his bike. He figured out what his acceleration was (3 m/s�), and how long (6s) it took to get to a certain speed from rest (0 m/s), but when Cole asks what his final velocity was, Dustin has forgotten. After some thought and research, Dustin concludes that he can find his final velocity placing his results in the equation:
When he does, he gets an answer of
18m/s! Wow! He can really pedal!
One day, Dustin is so wrapped up in finding out his acceleration, he forgot how far he travelled. By now, the library has just given him all the books on acceleration because he's been borrowing them so often, so he goes home and looks to see how he can find out what his displacement was. He finds the equation:
. If his initial velocity was 0m/s, his time was 500s and his acceleration was 1.5m/s�, what was his displacement?
187500 meters! Wow! He really went far today!!
Dustin still isn't satisfied. He know knows that amazing distance he biked, his displacement, his initial velocity and his time, but he can't remember (yet again) what his final velocity was. Back to that good old acceleration book! He just can't put it down! He discovers:
So when he places the numbers in their respective spots:
he finds that he was going 750m/s
All this talk of acceleration is starting to hurt his brain. He decides to take his mind off of it for a while. He bikes for 300 seconds starting from rest to a velocity of 4.5m/s. He doesn't know how far he got before he remembered about his English homework. Before he even opens his binder, he decides to check his acceleration book to see how far he went. The book tells him
So when he plugs in his numbers he finds he went 675m.
One day when Dustin is in a bike race, he can't keep his mind off of Physics and acceleration. Suddenly he looks stops, looks down, and realizes he's biked off a cliff. He begins to free fall. In the 3 seconds it takes him to fall, he calculates what his final velocity will be and the distance that he fell. So how did he manage to figure that out without having his trusty acceleration book with him? Well, he knew that his acceleration was due to gravity, and that it was -9.81 m/s�! Isn't he so smart (by the way, his final velocity was -29.43 m/s and his displacement was -44.145m)
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