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bandrockstar
 2 years ago
a particle moves along the xaxis so that its velocity at any time t is given by v(t)=3t^218t+24 and its position is given by x(t)=t^39t^2+24t+4.
A. For what values of t is the particle at rest?
B. Find the total distance traveled by the particle from T=1 to T=3.
Hint: the particle is moving to the left when v(t)<0 and to the right when v(t)>0.
bandrockstar
 2 years ago
a particle moves along the xaxis so that its velocity at any time t is given by v(t)=3t^218t+24 and its position is given by x(t)=t^39t^2+24t+4. A. For what values of t is the particle at rest? B. Find the total distance traveled by the particle from T=1 to T=3. Hint: the particle is moving to the left when v(t)<0 and to the right when v(t)>0.

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Narses
 2 years ago
Best ResponseYou've already chosen the best response.0a) v=0 for rest so solve the quadratic equation of v(t) b)sketch v(t) for t=1 to v=3 the combination of the area under/over the graph between the x axis is the distance traveled, you may have to do two integrations for this

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1I don't understand how to get these answers. I have an answer key, I just don't understand velocity at all. I am in precalculus and since it is the end of the year, my teacher is giving us a calculus packet so we can start learning. She has been gone every day since we've gotten it and she will be back tomorrow. I don't understand this velocity stuff at all.

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0@Narses for partb) why don't we apply directly to x(t) ?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0x(t) may be positive and negative so simply doing x(3)  x(1) may not work

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1I DON'T GET THISSSS

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0that would be the magnitude of the distance between the two points not the distance traveled, I was giving a more general case

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0Nope, not that Narses. the distance can get by absolute value @bandrockstar wait, after discussing, we will give you the correct instruction.

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0the total distance traveled may not be the distance between x(1) and x(3)

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0Ok, guide her steps, please

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0velocity as a function of time is what you given is describes the speed and which direction, so part a says when is it stationary, that is when the velocity (or speed) is equal to 0 such 3t^218t+24 =0

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Okay. I got that much now.

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1so the first step is to set v(t) equal to zero?

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1What am I trying to get out of setting it to zero? Like do I basically unFOIL it?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0basically yes use whatever method you know to solve quadratic equations

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1erm alright. Thanks hold on :)

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0by setting to zero you are telling the equation that the particle is at rest

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, That i can actually understand. So what is it after you equal it to zero

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0so for for part a you have 3t^218t+24 =0 that gives t^26t+8=0 by dividing both sides by 3 ( I guess you can solve is easier now?)

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1I don't understand what you put in parenthesis.

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0I said that you may be able to solve the equation now that we divided by 3?

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. is it 3(t2)(t4) ?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0yes, there is no need for the three as the other side is equal to 0 as 0/3=0

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Okay.. so where in the equation (t2)(t4) do I get my answer? What am I taking from it? The zeros?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0if (t2)(t4)=0 imagine a times b =0 how do we get that? what is a or b?

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Like the zeros being 2 and 4? I don't understand what I'm trying to get from this equation

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0the solution is that either A or B HAASSS to equal 0 so, t2=0 or t4 =0 such t=2 and 4

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, that's what I was thinking.

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1So t=2 and t=4 are the values for the particles at rest because thats the values where t=0. Correct?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0yes but a typo on your end is you want v=0 at the end

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1That's what I meant :P How do I do B?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0so you have an eqaution for the distance from 0 in terms of t, how would you approach it? any ideas?

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Would i be plugging in 1 and 3 somewhere? But I have to use the second equation? I'm just not sure how to do this stuff AT ALL. I have absolutely NO background on it. Sorry :/

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0its ok, when I first had answered I thought you had basic calculus but no problem, from part a you know that its stationary at t=2 and 4 so in the time period 1>3 the particle must change direction

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0as in the diagram shown it 'goes back on itself' so by simply finding the distance between point a and b where t =1 and 3 respectivly the particle will infact travelled further

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1How do we find the distance? Will the second equation be used?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0yes, so between t=1 and 2 the particle will be traveling in the same direction so we can take the distance between the two points and do the same with t= 2 and 3

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Okay. How do you find the distance between the two?

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0I need to go soon but work out the difference of x(1) and x(2) and add to the difference of x(2) and x(3) that is the answer,

Narses
 2 years ago
Best ResponseYou've already chosen the best response.0x(1)= put 1 into to t of x(t)

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1Thank you so much. I appreciate it very very very much :)

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1I am not getting the same answer as the key. I get 4 for the difference of x(1) and x(2) and I get 2 for the difference of x(2) and x(3). I am getting 2 when I add them together. The answer on the key is 6 units. I don't understand what I'm doing wrong and I've checked my arithmetic twice.

Universidad
 2 years ago
Best ResponseYou've already chosen the best response.0Since you have the velocity at time v (t) = 3t ^ 218t +24, then the particle will be at rest when v (t) = 0, that is, you have to find the values of time t for which 0 = 3t ^ 218t +24, so you have to solve the quadratic equation. So 0 = 3 (t ^ 26t +8) Therefore 0 = (t4) (t2), so that t = 4 and t = 2. Thus at t = 2 and t = 4 the particle will be at rest.

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1I already knew that.

bandrockstar
 2 years ago
Best ResponseYou've already chosen the best response.1The answer is 6 units.

Universidad
 2 years ago
Best ResponseYou've already chosen the best response.0absolute valor (2)+absolute Valor(4) =6 It is not a vector (Start PointFinal Point), but a scalar, sum of paths.

Universidad
 2 years ago
Best ResponseYou've already chosen the best response.0v (t) = 3t18t +24 ^ 2 = 3 (t4) (t2) is> zero when both (t4) and (t2) are positvos or when negative. And t4> 0 when t> 4 and t2> 0 when t> 2, so that both are positive parpentesis if t> 4 or both parentheses are negative if t <2, and both are negative paréntsis] 2 , 4 [. Has to calculate the distance of 1 to 2, d1, 2 = x (2)x (1), this being the distance to the right (positive sign) and then the distance of 2 to 3, d2, 3 = x (3)x (2), this being the distance reccorrida left (negative sign), Suma refusal distances more positive one and that is the total distance traveled. x (2) = 2 ^ 39 * 2 ^ 2 +24 * 2 +4 = 24, x (1) = 1 ^ 39 * 1 ^ 2 +24 * 1 +4 = 20 d1, 2 = x (2)x (1) = 2420 = 4 That is d1, 2 = 4 The distance to the right x (3) = 3 ^ 39 * 3 ^ 2 +24 * 3 +4 = 22 d2, 3 = x (3)x (2) = 2224 = 2 The distance to the left from the start point So the displacement vector is Right + Left = 42 = 2 as right shift vector, but if you want the total distance not as vector but a scalar, D=4+2=6
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