# Instantaneous velocity and acceleration as functions of time

jensson

## Homework Statement

The position of an object as a function of time is given by x = At^2 + Bt + C
A = 8 m/s^2
B = 6 m/s
C = 4 m

v = u + at
a = v/t

## The Attempt at a Solution

I don't even know how to set this up!

zhermes
how does velocity relate to position?
how does acceleration relate to velocity?

jensson
velocity is the change in position with respect to the change in time and acceleration is the change in velocity over time.. is that what you mean?

this question was on a quiz and I got it wrong.. I can't seem to make it make sense in my head. I have the answers and I still can't figure out how to get there.

zhermes
You're exactly right so far! So what mathematical process gives you the change of something (i.e. position 'x') with respect to a variable (i.e. time 't')?

jensson
I can only think of putting that into equation form

V = dx/dt

but the position is given has a quadratic equation.

V = 8t + 6t + 4/t

but that doesn't seem right

zhermes
You have the right idea, you're just not taking the derivative correctly.

$$x = At^2 + Bt + C$$
$$v = 2At^1 + Bt^0 + 0$$ You always decrease the power of the variable by one--but if there is no variable, then the derivate is zero---in other words: if there is no variable, it is constant, and thus the slope/change is zero.
Then the 'B' term becomes just B, and the C term drops out (is zero). ====>
$$v = 2At + B$$
then you repeat to find the acceleration, and plug in to find the values.

Does that make sense? Make sure you review your derivatives :)
What does the acceleration equal?

jensson
I am in calculus I right now and taking physics. My advisor said I should be fine taking them at the same time, but I seem to be completely lost!

zhermes
Yeah, that's definitely an extra challenge, but its totally doable.
They key is just not getting overwhelmed by it; go one step at a time, one problem at a time, one concept at a time.

Does the derivative I did above make sense?

jensson
hah I already do feel overwhelmed by it :-/
A 2 problem quiz every thursday and thanks to this problem here I got 1/2 wrong :(

I can see the pattern in your steps, but I have not studied derivatives yet so I don't know why it was done

zhermes