Sunday, August 23, 2009
Post #1
In Calculus class last week we learned about average speed, instantaneous speed, and Product rule and the Quotient Rule. I basically understood dervatives and I understand the Product and quotient rule; but I am not good at doing INstantaneous speed and average speed. I understand Average speed up to the m=y2-y1/x2-x1 then on instantaneous speed i don't even know where to start
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Mabile,
ReplyDeleteMake sure you have 250 words!
so for Average Speed:
ReplyDeleteTake the problem they give you then take two numbers from the problem and make them a point. For example:
A water balloon is dropped and falls at y=4.9t^(2)m in (t) seconds. Find the average speed during the first 3 seconds.
so you know that your point will be (0,3) because it's the FIRST THREE SECONDS. so you plug in the 0 in order to get the answer for t1. [you should get 0] Then take the 3 from the point and plug it in, in order to get the answer for t2. [you should get 44.1]
now, the ANSWER you got AFTER you pluged it in goes AT THE TOP. it'll be t2 - t1
it should be 44.1 - 0
this will go over the point..remember instead of x and y it could be known as t1 and t2.
take t2 and subtract t1 from it.
it should be 3 - 0
now that you have both t2 and t1 for both things, the one that you got when we pluged it in...the one that ended up being 44.1-0...you put that at the top of the equation and then put the point which ended up being...3-0...as the denominator. giving you:
44.1 - 0
________
3 - 0
whis is 44.1 divided by 3 giving you
14.7 meters per second for the average velocity
[dont forget the meters per second!!]
now for instantaneous speed:
ReplyDeleteall you need to do is take the derivative of the equation they give you then plug in what they give you "t" is equal to.
for example: [number 29 on the HUGE packet]
Given the position equation: s(t)=t^(2)-3t-1, find the instantaneous velocity at t=3.
so all you need to do is take the derivative which is:
2t-3
so now just plug in 3 for all the "t"s. giving you:
2(3) - 3
so that's 6 - 3
which is 3!
THATS YOUR ANSWER!
Average speed is a pretty simple concept. Take for instance the example An anvil falls off the roof onto Ryan G's head. What is it's average speed during the first two seconds if y=16t^2 describes the fall.
ReplyDeleteYou are given the time frame which is the first two seconds. You plug both numbers, (0 and 2) to the formula given y=16t^2 to find your y1 and y2. once your the two x's and two y's you just plug into to slop formula (m=y2 - y1 all over x2 - x1. Your y1 is 16(0)^2 and your y2 will come out as 16(2)^2. Therefore, m=64-0 over 2-0 which is 32. Box that off and that is your answer for average speed, also known as slope :)
For instaneous speed, you start off by taking the derivative of the equation you're given. Once you have the derivative, you use the formula f(x+h)-f(x)/h, plugging in t for all x's. Next all you have to do is algebra and you should end up with only one h in the problem. From there, you plug in 0 for h because the limit approaches 0 and then thats your answer.
ReplyDelete