Deriving acceleration from a position function

[uchicago2012]

Homework Statement

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?

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.

 

[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. :)