# Math Help - Displacement of a particle

1. ## Re: Displacement of a particle

Originally Posted by srh
I'm studying mechanical engineering, I've got only a basic grasp of calculus from what I've been able to teach myself online.
what school offers a course of study in mechanical engineering without concurrent enrollment or completion of formal courses in calculus?

2. ## Re: Displacement of a particle

A very very poor one.

3. ## Re: Displacement of a particle

These problems are so much easier to write out if you do some trig to begin with. Here the 3 and the 4 are a bit of a giveaway indicating a 3,4,5 triangle. Taking the liberty of changing the d to the more usual s,

$s=3\sin(40\pi t)-4\cos(40\pi t)=5\left(\frac{3}{5}\sin(40\pi t)-\frac{4}{5}\cos(40\pi t)\right)$

$=5\sin(40\pi t-\alpha),$ where $\cos\alpha=3/5, \sin\alpha=4/5, \tan\alpha=4/3.$

That doesn't get you pass the calculus however.

Velocity $v=\frac{ds}{dt}=200\pi\cos(40\pi t-\alpha),$

Acceleration $a=\frac{dv}{dt}=-8000\pi^{2}\sin(40\pi t-\alpha).$

The particle will be at rest when the velocity is zero, that is, when $200\pi\cos(40\pi t-\alpha)=0,$ etc.

4. ## Re: Displacement of a particle

Hi,

3sin(40)+ 4 cos(40) =5 but multiplying by pi or t?

5. ## Re: Displacement of a particle

Originally Posted by srh
3sin(40)+ 4 cos(40) =5 but multiplying by pi or t?
I hope, no pray, that you have none of your personal money going out for this program of study.
If you are, it is a waste!

6. ## Re: Displacement of a particle

I do, and yes it is!

But that's besides the point I need to learn.

7. ## Re: Displacement of a particle

Trigonometry | Khan Academy Video Course

Calculus | Khan Academy Video Course

8. ## Re: Displacement of a particle

It's ok I think I may be close to understanding.

3 x sin(40 pi radians x time)?
In which case I'm looking for the length of the hypotenus (5) x 40 pi radians x time?

So it's simple harmonic motion?

9. ## Re: Displacement of a particle

It's ok I think I may be close to understanding.
In the end you will just understand this question, but when thrown another question similar to this you will get it wrong..

Trust me I am talking from personal experience, it never pays.

You should watch those Khan videos, the guy is brilliant.

Here is another link to the physics Section:

10. ## Re: Displacement of a particle

Yeah I have been on this website before, unfortunately I don't have time to sit through all those videos. I need to have this question and others finished today.

11. ## Re: Displacement of a particle

Ok I've got it

The way it was written was throwing me off, I also confused Pi with Pi radians.