# Finding graphs from motion model

## Homework Statement

I have a problem where I am given the model:

x(t) = 2.5 - 2t + 0.8t2

From this I have to determine the x vs t, v vs t, and a vs t graphs. I have to do this without plotting points. Specifically it says, "Draw the graphs by identifying and interpreting the parameters, not by plotting points."

## Homework Equations

None, I don't think, except y=Ax2+Bx+C

## The Attempt at a Solution

I wish I could say I have an attempt, but I honestly don't know what to do. What am I looking for? This is algebra based physics, so I can't simply use calculus. Just a little guidance would be awesome.

Thank you so much for any help!

ehild
Homework Helper

## Homework Statement

I have a problem where I am given the model:

x(t) = 2.5 - 2t + 0.8t2

From this I have to determine the x vs t, v vs t, and a vs t graphs. I have to do this without plotting points. Specifically it says, "Draw the graphs by identifying and interpreting the parameters, not by plotting points."

## Homework Equations

None, I don't think, except y=Ax2+Bx+C

## The Attempt at a Solution

I wish I could say I have an attempt, but I honestly don't know what to do. What am I looking for? This is algebra based physics, so I can't simply use calculus. Just a little guidance would be awesome.

Thank you so much for any help!

The independent variable is t, the dependent one is x. You are right, x(t) is the same kind of curve as y=Ax2+Bx+C. What is the name for that type of curve?

What kind of motion is when the displacement is quadratic in time?

ehild

Last edited:

It would be a parabola.

'What kind of motion is when the displacement is quadratic in time? '

Projectile? Which confuses me because the paper says the model is describing the position of a particular boat as a function of time.

ehild
Homework Helper
Something like projectile, but more general - think of the acceleration...

ehild

Oooh, motion at constant acceleration?

ehild
Homework Helper
Oooh, motion at constant acceleration?

Yes! You certainly know the formula of the displacement in terms of time...

ehild

Xf=xi+(vx)iΔt+(1/2ax)(Δt)2

So.. this one?

ehild
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Xf=xi+(vx)iΔt+(1/2ax)(Δt)2

So.. this one?

Yes. Now you can find the value of ax, vxi and xi, don't you?

ehild

Ok, got it! ax=1.6m/s2, vxi= -2 m/s, and xi=2.5m

ehild
Homework Helper
Right! a is a constant, and how does v change in time?
It is easy to plot a(t) and v(t), and you know that x(t) is a parabola. Can you find its peak?

ehild

V changes at a constant rate of 1.6 m/s2.

And the peak of the parabola is (1.3s, 1.3m)?

ehild
Homework Helper
V changes at a constant rate of 1.6 m/s2.

Yes, but what is the v(t) function? Remember, there is some initial velocity.

And the peak of the parabola is (1.3s, 1.3m)?

Close, but not quite so. The peak of the parabola is at time when the velocity is zero. When does that happen?

You can also write up x(t) in the form x= a(t-k)2+b, then the peak is at t=k, x=b.

ehild