Using Calculus to Solve for Time in a Particle's Position Function

[morphine]

Homework Statement

(Sorry I don't know how to insert nice looking equations)

If the position function of a particle is given by
s = t³ - 4.5t² - 7t, t >= 0
, the particle reaches an instantaneous
velocity of 5 m/sec when t =
1
2
3
4
5

Homework Equations

The Attempt at a Solution

Well, the problem I'm having is how to do this to find t instead of finding the velocity. If I attempt to find the derivative, I always get stuck at something like:

lim _{h -> t} [(t+h)³ - 4.5(t+h)² - 7(t+h)] - [t³ - 4.5t² - 7t] ALL OVER h

I can play with that a little bit, but it never gets anywhere. thanks

 

[Mark44]

Assuming that you have to use the definition of the derivative, expand your (t + h)³ and (t + h)² terms and then combine all like terms in the numerator. There should be some simplification so that you can then divide by the h in the denominator. Finally, take the limit as h --> 0 and you will be left with your derivative.

 

[dacruick]

Well you need to find the derivative. I can tell you the answer is 4 but you should find it for yourself. If that is where you get stuck, expand it out and cancel out like terms. What i mean by that is calculate (t+h)(t+h)(t+h) and then find 4.5(t+h)(t+h) and so on. You will see that all terms without the h cancel out, and you are able to divide everything by h.

Keep in mind that the answer you will then have is now a speed function, not a position function. If you are still stuck post again.

 

[morphine]

OK, I did that, and assuming my algebra was right I got 3t² - 9t - 7

And here I'm stuck again. Do I just set that equal to 5 and solve?

 

[Mark44]

That is the correct value of s'(t). Now evaluate s'(t) at t = 1, 2, 3, 4, and 5.

 

[morphine]

Awesome now I see. Thanks for the help Mark and dacruick.

Ill probably have a few more questions over the next few hours.