# Thread: Speeding up with a given function

1. ## Speeding up with a given function

A car's position is given by $\displaystyle d(t)=2t^3-24t^2+78t-56$, find when it is speeding up and speeding down.

I'm a little confused if it means the acceleration (2nd derivative) or velocity (1st derivative). I'd have thought acceleration, but the 2nd derivative is only positive when $\displaystyle t>4$, but when looking at its graph (http://www.wolframalpha.com/input/?i=2x^3-24x^2%2B78x-56), you' assume it was speeding up after it hit its maximum value until the inflection point.

Was I right for thinking it speeds up after it hit the max/min?

2. Originally Posted by youngb11
A car's position is given by $\displaystyle d(t)=2t^3-24t^2+78t-56$, find when it is speeding up and speeding down.

I'm a little confused if it means the acceleration (2nd derivative) or velocity (1st derivative). I'd have thought acceleration, but the 2nd derivative is only positive when $\displaystyle t>4$, but when looking at its graph (http://www.wolframalpha.com/input/?i=2x^3-24x^2%2B78x-56), you' assume it was speeding up after it hit its maximum value until the inflection point.

Was I right for thinking it speeds up after it hit the max/min?
The term "speeding up" refers to an increasing speed. Thus you are looking for a region of the graph where |v| is increasing. Similarly for "speeding down" you are looking for when |v| is getting smaller.

Mathematically speaking take the derivative of your displacement function to get the velocity. Then find
$\displaystyle \displaystyle a = \frac{d|v(t)|}{dt}$

-Dan

3. Originally Posted by topsquark

Mathematically speaking integrate your displacement function to get the velocity. Then find
$\displaystyle \displaystyle a = \frac{d|v(t)|}{dt}$

-Dan
Integrate the displacement function to find velocity?

4. Originally Posted by e^(i*pi)
Integrate the displacement function to find velocity?