Simple displacement and acceleration question

AI Thread Summary
The discussion revolves around finding displacement and average velocity from the position function s(t) = t^2 - 3t + 2 over the interval 0 to 2. Participants clarify that displacement is the change in position, while average velocity is the change in position divided by the change in time. The derivative 2t - 3 represents the instantaneous velocity, not the average velocity or acceleration. To find the displacement, one must evaluate s(t) at the endpoints of the interval, specifically at t = 0 and t = 2. The confusion stems from mixing up the concepts of position, displacement, and velocity, emphasizing the need to apply the correct definitions and calculations.
jaydnul
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Homework Statement



Find the body's displacement and average velocity for the given time interval.

s=t^2 -3t +2, 0<=t<=2


Homework Equations



d(displacement)/d(time) is for the acceleration right?


The Attempt at a Solution



So here is my problem. I got 2t-3 for the derivative, but i don't really know how to apply it to the question. I feel like i need just one value for t in order to find the displacement and velocity at that point, right? So how do i incorporate a full interval, 0 to 2? The back of the book says -2 for displacement and -1 for acceleration, but i have no clue how that is the case when you have multiple values of t. I would have just said the 2t-3.
 
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What does the given equation represent? Position? Velocity? Acceleration?

The change in POSITION(not displacement, they are related but not the same) over the change in time is velocity. the change in velocity over the change in time is accleration.

d(POSITION)/d(time) is not acceleration. When you get confused on these, try and just think about the units you would be working with it. X(meters) over T(seconds) That is m/s which is velocity. I think you are getting position and displacement confused. Position is simply where something is at any given time. Where as the displacement is Δx or the change in its position. Additionally, you are dealing with the CHANGE in time. That being said, yes. It is necessary to have more than one value for t.
 
Last edited:
lundyjb said:
So here is my problem. I got 2t-3 for the derivative, but i don't really know how to apply it to the question. I feel like i need just one value for t in order to find the displacement and velocity at that point, right? So how do i incorporate a full interval, 0 to 2? The back of the book says -2 for displacement and -1 for acceleration, but i have no clue how that is the case when you have multiple values of t. I would have just said the 2t-3.
There's no need for calculus here. You are given the position (s) as a function of time.

What's the definition of displacement?

What's the definition of average velocity? (They want velocity, not acceleration.)
 
What is s(t) when t = 0? What is s(t) when t = 2?
 
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