# Homework Help: Deriving acceleration from a position function

1. Aug 31, 2010

### uchicago2012

1. The problem statement, all variables and given/known data
A particle moves along the y axis according to y(t)=(3.5 m/s2)t2 - (9.0 m/s)t + 5.0 m.
(a) What is the particle's velocity as a function of time?
(b) What is the particle's acceleration at t=2.0 s?

3. The attempt at a solution

I was wondering about b- I derived:
dy/dt = (7 m/s2)t - 9.0 m/s for the velocity function
and then
dv/dt = 7 m/s2 for the acceleration function.

So the acceleration is constant, right? I'm finding seemingly irrelevant questions make me paranoid.

2. Aug 31, 2010

### MitsuShai

Yes, you just showed that the acceleration is constant. In fact you can check with a graphing calculator by applying the knowledge you learned in class.
In fact when you graph the y(t) equation you get a upwards parabola. Then the v(t) graph will be a positive line. Thus the a(t) graph is constant.
My calculator says you are right. :)