Question

Having trouble figuring out this question: Find the equation for a linear trajectory that starts at (0, 50) and ends at (200, 350), where the speed is constant 25 m/s. Be sure to specify the time interval.

Answer 1

Is this calc based physics?

Answer 2

Actually its a Calculus 3 question using parametric equations I think

Answer 3

ok gimme a sec

Answer 4

Ok so what do we know about speed?

Answer 5

It's a constant 25 m/s

Answer 6

What else do we know? The derivative of ______ is _______. ______ is the ________ of _______.

Answer 7

not sure, all that's given is two sets of points.

Answer 8

ok, so it's a definition. The derivative of position is velocity. Speed is the absolute value of velocity.

Answer 9

So given this, can you think of a way to derive the position function?

Answer 10

Integration comes to mind.

Answer 11

good idea

Answer 12

so what are the two possibilities for the velocity?

Answer 13

Still not sure what to integrate though since I'm not given a function to integrate just two points.

Answer 14

but the velocity is constant right? v(x)=|25|

Answer 15

Oh! So if I integrate that i'd get 25t which would be the inside of the x = cos(25t) and y = sin(25t)? Am I on the right track? using the two sets of points I could find the radius i'm assuming? Not sure how

Answer 16

wait no no, it's linear, you're over complicating it

Answer 17

it's just a line. It has a constant velocity. A constant velocity = a _______ slope.

Answer 18

True! Bah.. but if Integrate the speed i'd get 25t.

Answer 19

right but what did you forget about with that indefinite integral?

Answer 20

25t + c for the constant of course!

Answer 21

I understand that much of it, the thing that confuses me is what the two sets of points are for. I'm trying to understand why those are given. As well as it says "Equations" not just an Equation.

Answer 22

it only says eq. and the points are for you to determine the time.

Answer 23

what does c=? this is a trick question

Answer 24

solving for c=? You would get c =-25t not sure if that's what you're asking

Answer 25

how did you get that??

Answer 26

From what we integrated above, 25t + c, I just solved that for c. I'm probably wrong

Answer 27

yea, I'm not quite sure how you solved it... I can't work it backwards but no, that is not correct. Remember the points are x and y positions but they are also just lines(this is where the parameterization comes in). They can be represented as <x(t),y(t)>

Answer 28

so if we assume that at t=0 <x(t),y(t)>=<0,0>

Answer 29

we can eliminate he c right?

Answer 30

oh wait starts at <0,50> my bad

Answer 31

so at t=0 x(t)=? y(t)=? And (do you follow? or am I confusing you?)

Answer 32

I'm a bit confused a bit because I haven't taken physics or seen much of this material in any of my Calculus classes so I haven't seen stuff like this except a week or two in Calculus 2 before the semester ended. Though the last comment would we use what we found by integrating? x(t) = 25t and y(t) = 25t?

Answer 33

Ok my bad, sorry, so you already integrated you don't need to do it again. You just need to write the y=mx+b form of the line that you integrated. So we know m=? the intercept for y=? for x=?

Answer 34

i also recommend http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

Answer 35

it got me through calc

Answer 36

Still confusing me a bit, but from whats given in the problem couldn't we find the slope from the two sets of points. and y int is 50, not sure about x

Answer 37

not easily, it gives the velocity so you can look at that piece of info and use it.

Answer 38

y int is correct

Answer 39

How would I go about finding the x intercept?

Answer 40

what is x at t=0?

Answer 41

would it just be 0?

Answer 42

yuppers

Answer 43

so the parametric eq would be?

Answer 44

Unsure of what the slope is or would that be what we found when I integrated 25t?

Answer 45

no the derivative is the slope right? so when you find a parametric eq you are finding the position function. When you find the position function's derivative you get velocity

Answer 46

x(t)=25t that's it. it's that simple :)

Answer 47

was just about to write that! haha

Answer 48

good :) sorry I'm getting tired so I might just try to speed things up at times

Answer 49

so what is y(t)?

Answer 50

That's fine! so for y(t)= 25t+50

Answer 51

yup now you have an equation and an end pt and you need to find at what t it reaches that end pt. andddd GO! :P

Answer 52

so it ends at (200,350) would I just do this 200=25t and 350=20t+50 and solve for t? or again am i doing things wrong... Sorry again I feel stupid

Answer 53

nope that is 100% correct

Answer 54

you should get the same value

Answer 55

wait... what did I do wrong

Answer 56

I typed in one wrong above

Answer 57

i put 20 in the second one where it should be 25

Answer 58

no not that, are you sure the question didnt say (200,250)? or (300,350)?

Answer 59

The question is (200,350)

Answer 60

starts at (0,50) and ends at (200,350)

Answer 61

hmmmm

Answer 62

It could be a typo by my teacher he does that a lot on his handouts he gives us as well.

Answer 63

But from what I got above 8 from first one and for the second one 15?

Answer 64

Yea, because the answer doesn't exist otherwise

Answer 65

not with a constant slope that is

Answer 66

I'll send him an e-mail about it

Answer 67

How did you solve for t??

Answer 68

you would do like i said right? 200=20t which just divide 200 by 20 and you get 10

Answer 69

300/25=?

Answer 70

200/25?

Answer 71

I am confusing the hell out of my self, it should be 200/25 bah

Answer 72

Which is 8?

Answer 73

lol yea you're tired too
yea but the second one

Answer 74

for the second one 300=25t+50 subtract the 50 so you get 250=25t

Answer 75

then divide by 25

Answer 76

it should be 350 haha i am tired

Answer 77

350-50?

Answer 78

ud get 300=25t lol

Answer 79

lol

Answer 80

and that would give 12

Answer 81

ok that sounds better

Answer 82

yea sorry lol.. the question below on my sheet is using constant speed of 20.. i was reading it off of there.. and then writing it here, but its 25.

Answer 83

so you see the answer DNE

Answer 84

they have to be equal

Answer 85

so if it was equal and both answers were 8 would the interval of to be between 0 and 8 then

Answer 86

yea

Answer 87

inclusive

Answer 88

don't forget units

Answer 89

ahh i'll have to ask him then. When I see him if he doesn't reply by e-mail before my class Wed

Answer 90

for time it would be in seconds?

Answer 91

ok well best of luck. I'm \[ \color{maroon}{reallllllllllllllllllllllllllllllllllllllllllllllllllyy}\] \[ \huge{ {\color{red} TIRED}}\]

Answer 92

yep seconds

Answer 93

ok thank you :) You were a big help! i'd still be stuck on this problem without you!

Answer 94

np just tag me if you ever need help again :) also if you don't mind, you can fan, medal, or testimonial if you have time

Answer 95

I fanned you just now :D i'll medal you too!

Answer 96

lol perfect timing, thanks I appreciate it. I use this for job credibility when I tutor.

Answer 97

Very nice! :) Thanks again!

Answer 98

have a nice night. sleep well