Simple displacement and acceleration question

[jaydnul]

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.

 

[MostlyHarmless]

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.

 

[Doc Al]

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.)

 

[SteamKing]

What is s(t) when t = 0? What is s(t) when t = 2?

 

[Nickie]

As a scientist, it is important to understand the concepts of displacement and acceleration in order to accurately solve problems like this. In this case, the body's displacement and average velocity can be found by taking the derivative of the given equation, s=t^2 -3t +2, with respect to time. This will give us the velocity equation, v=2t-3.

To find the average velocity, we need to take the integral of the velocity equation over the given time interval, 0 to 2. This will give us the displacement equation, d= t^2 -3t +2. Plugging in the values of 0 and 2 into this equation, we get a displacement of -2, which is the same value given in the back of the book.

As for the average velocity, we can use the formula v_avg= (d_final - d_initial)/t_final - t_initial. Plugging in the values of -2 for d_final, 0 for d_initial, 2 for t_final and 0 for t_initial, we get an average velocity of -1. This is also the same value given in the back of the book.

In conclusion, it is important to understand the concepts of displacement and velocity in order to solve problems like this. By taking the derivative and integral, we can accurately find the displacement and average velocity for the given time interval.