Particle Motion Problem?

purplemarmose

1. The problem statement, all variables and given/known data
Moves at G(f)=t^2-4t+3
a. Find displacement at 2 sec
b. Find average velocity at 4 sec
c. Find instantaneous velocity at t=4
d. Find acceleration at t= 4


2. Relevant equations
Instantaneous rate of change
Displacement


3. The attempt at a solution
f'= 2t-4 (So this would be the velocity then?)
f''=2 (Acceleration?)

How do I go about finding it at specific values? Just plug it in?
For example...
Find average velocity at 4 sec:
2(4)-4= 4

Infinitum

Hi purplemarmose! Welcome to PF

This is a physics problem, it would be more relevant to post it in the Introductory Physics section.

Anyway, I'll take a stab at it.

What you've done is correct. The first derivative does indeed give you the instantaneous velocity(instantaneous is important!) with respect to time. The second derivative gives the instantaneous acceleration. Of course, you have to plug in the time values for respective answers

purplemarmose

Thanks for your greeting! This problem was actually given to me by my calculus teacher! However, I do know it that it is relevant to physics. Thanks so much!

HallsofIvy

It might be helpful to at least copy the problem correctly. Surely it does not say G(f) and then give a formula in t. Then later, you talk about "f(t)". And "Find average velocity at 4 sec" makes no sense- an average velocity has to be over a given interval of time. I suspect you mean the average velocity between t= 0 and t= 4 although it might be between 2 and 4 since you were also asked for the displacement at t= 2. The derivative of a position function is a instantaneous velocity at the given value of t. And acceleration is the second derivative. It also should be evaluated at a given value of t, but here, the acceleration function is a constant.

Do you know the definition of "average velocity" between two values of t?