Jet Engine Displacement, Avg. Velocity & Instantaneous Velocity Calculation

[PHYSICS!!!:-)]

Instantaneous Velocity?? (stupid question i bet...)

Homework Statement

A jet engine moves along an experimental track. Its psoition as a function of time is given by the equation x=At^2+B. A=2.10 m/s^2 and B=2.80 m. A)Determine the displacement of the engine during the time interval from t(sub1)=3.00s, to t(sub2)=5.00s. B)Determine the Avg. velocity during this time interval C.)Determine the magnitude of the instantaneous velocity at t=5.00s.

Homework Equations

The Attempt at a Solution

I can't even try to attempt this, I don't know calculus, and cannot do the derivatives for the Instantaneous velocity. I need A.)how to do the derivatives, and B) part C for this question
Thanks :-)

 

[NBAJam100]

Well, there are many rules of taking derivatives, but in this case, you should be fine if you know this rule:

say y = x^n ---> take y'= the derivative of y

So y'= n*x^(n-1)

That is the general rule for taking a derivative, so you just bring the power its raised to down to the front and then subtract one from that value up top.

So ex:

if y= x^2, then y'= 2x, because you bring the 2 down, and then subtract 1 from 2 to get 1.

To do part C you would just take the derivative of that function with respect to t instead of x like i did in the example above, so in other words, every t you see, do what i did above. If you have a constant (aka a part of the equation with no t, it just goes to zero). That will give you the instantaneous velocity function, so you can just plug the time you want the instantaneous velocity for into that function.

 

[Saladsamurai]

If you don't know Calculus and you are allowed to take this course then I will assume the only rule (or least one of the only rules) you will need is the Power Rule

If y is some function of x, we represent its derivative as \frac{dy}{dx}. Though this looks like a fraction, it is not...well it kind of is...but that is neither here nor there for now.

It is pronounced literally as it looks: dee-why, dee-ex, and for practical purposes is a really tiny change in y with respect to a really tiny change in x.

If you have y as a polynomial function of x (which you do) that looks like this: Ax^n[/itex] then its derivative is n*Ax^{n-1}

So if your function is let's say y=4x^3 then its derivative \frac{dy}{dx}=3*4x^{3-1}=12x^2

 

[Ebola0001]

I think you are over complicating things for yourself

a) displacement of engine in interval between 3 and 5 seconds

this is just asking how far it moved in this time, find its position at 3 seconds, find its position at 5 seconds, subtract where it was from where it is to get the displacement during this interval.

b) find the average velocity during this interval

the average velocity is the distance over time of an interval. you have the distance from part a. find the length of time of the interval subtract t₁ from t₂, and write the fraction

c)what is the velocity AT exactly 5 seconds

this is a bit more fun, it involves the derivative (as stated by NBAJam, and SaladSamurai)

Position = At² + B

the B is indicating the starting position and has no bearing on the speed so it is set to 0 ( this is because it does not have a m/s or m/s² with it only an m, if it has a m/s it would be the starting speed before acceleration.

so you only have At²

as mentioned the derivative of an exponent is n^x => x * n^x-1.

so in your case it would be 2 * At ^2-1 = 2at

set t to 5 seconds, set a to the given value and evaluate.

hope this helps :)