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help7244

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Aug 18, 2009
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the velocity of an object is given by the function
v(t)=t^3 - 14^2 + 45t
find all vaules of t when the particle is at rest


i think you put 0 at v(t), but do you also put 0 at all other t's that your not solving for
 


Hi 7244:

Nope. That results in 0 = 0, which is true, but not very interesting.

Also, I'm not sure what you mean by "all other t's that you're not solving for". This leads me to think that you might not have a good understanding of functional relationships between numbers. I'm going to include some review.

t is a single variable. There are not different "types" of t. For example, if the variable t takes on the value 5 seconds, then t = 5 anywhere it appears. So, there's only one variable to solve for, in this exercise.

You need to solve for t such that the value of the given polynomial is zero.

t and v(t) are two different variables; the former represents elapsed time, and the latter represents speed.

Function v gives us a formula for finding the object's velocity, if we know how much time has elapsed from some reference point t = 0.

If we substitute zero for t, then function v gives us the velocity at that time (i.e., at the very instant when time starts to elapse: t = 0).

v(0) = 0^3 - 14(0)^2 + 45(0) = 0 + 0 + 0 = 0

The velocity is zero when t is 0, so the object is not moving at time t = 0.

I just answered the question: "WHAT is the velocity at time zero?".

The question: "WHEN is the velocity zero?" is entirely different because the object might start and stop (and start and stop some more) as time elapses. In other words, there might be multiple times when the velocity is zero, but there is only one velocity when time is zero.

To understand this is to understand the difference between a dependent variable and an independent variable, as well as the concept of functions.

Finding all of the times when the object is at rest is the question in your exercise.

Again, a value of t represents some amount of elapsed time.

A value of v(t) represents the corresponding velocity at this time.

Since we're interested in the times when the velocity value is zero, we substitute zero for v(t) only, and then solve for t.

t^3 - 14t^2 + 45t = 0

(NOTE: You typed 14^2, but I'm guessing that's a mistake, so I changed it to 14t^2. Please use the [Preview] button to proofread before clicking [Submit].)

Next, to solve for t, notice that each term in the polynomial t^3 - 14t^2 + 45t contains a factor of t. Can you factor it out?

If so, you'll end up with one factor of t and a second factor that's a quadratic polynomial.

Set each of these factors equal to zero and continue.

If I wrote anything that you do not understand, then please ask! 8-)

Otherwise, show whatever work you can or tell us what you're thinking, if you'd like more help, so that we might determine where to continue helping you.

Cheers,

~ Mark

 
ok im little confused on how to separte, or factor them as there is no 4th term. i would still have 3 sets right. but would i separate the 45 into 2 terms before i do that...
but besides that i understand the problem
 
help7244 said:
… im little confused on how to … factor … as there is no 4th term …
Click to expand...


Hey there:

Again, I'm confused, too. I'm not sure what you're thinking about the number of terms. Whether there's two, three, four, or more terms is not relevant to the factoring, in this exercise.

We want to factor the cubic polynomial t^3 - 14t^2 + 45t.

Maybe, it will help you, if I rewrite the polynomial to show the common factor t in each term.

(t)(t^2) - (t)(14t) + (t)(45)

Can you factor this expression to get the following form?

(t)(at^2 + bt + c)

 
yeah i know how to do that.but dont i need 3 sets of Parenthesis to solve the probelm
 
so would it be
(t)(t-9)(t-5)
then set (t)=0 (t-9)=0 and (t-5)=o and ill get my answer
 
help7244 said:
… then set (t)=0 (t-9)=0 and (t-5)=o and ill get my answer
Click to expand...


Yes.

(I suggest you review the Zero Product Property; perhaps, you can find it listed in the index of your textbook.)

BTW, the parentheses above are not needed.

t = 0

t - 9 = 0

t - 5 = 0

 
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