integral: given velocity, find total distance traveled
- Thread starter mathhelp
- Start date
skeeter
Elite Member
- Joined
- Dec 15, 2005
- Messages
- 3,216
not a solution, but almost one.
if the object had a velocity v = sin(t), then it would travel the distance shown the table
0 to pi/2 -> 1 unit of distance
0 to 2pi/2 -> 2 units of distance
0 to 3pi/2 -> 3 units of distance
0 to 4pi/2 -> 4 units of distance
... and so on.
now, think about the distance traveled if its velocity were v = 5sin(t).
- Joined
- Feb 4, 2004
- Messages
- 16,582
Until the exercise makes sense, it is unlikely that a solution will be derived (and most legitimate tutors don't just "do" students' work for them, anyway).
Would it be correct to assume that "5sin(t)" is v(t), from which you are attempting to find the distance through integration?
Would it be correct to assume that "0~(pi/2)" means "the integral over the period from t = 0 to t = pi/2"? (You didn't define your non-standard notation, so you're requiring that we guess.)
Would it be correct to assume that you are asking for the distance travelled between 13pi (which is the simplification of (26pi)/2, as the tutor noted) and some fixed time that you haven't yet provided?
Please provide the rest of the necessary information for this exercise. When you reply, please show everything you have tried so far.
Thank you.
Eliz.
Would it be correct to assume that "5sin(t)" is v(t), from which you are attempting to find the distance through integration?
Would it be correct to assume that "0~(pi/2)" means "the integral over the period from t = 0 to t = pi/2"? (You didn't define your non-standard notation, so you're requiring that we guess.)
Would it be correct to assume that you are asking for the distance travelled between 13pi (which is the simplification of (26pi)/2, as the tutor noted) and some fixed time that you haven't yet provided?
Please provide the rest of the necessary information for this exercise. When you reply, please show everything you have tried so far.
Thank you.
Eliz.
revised
A dog is running along a fence with velocity (in feet per second) v(t)=5sin(t).
Using the fact that the integral from 0 to (pi/2) of sin(t) dt = 1
Find the displacement of the dog after (26pi)/2 seconds.
Find the total distance traveled by the dog after (26pi)/2 seconds.
hope this would verify confusion
A dog is running along a fence with velocity (in feet per second) v(t)=5sin(t).
Using the fact that the integral from 0 to (pi/2) of sin(t) dt = 1
Find the displacement of the dog after (26pi)/2 seconds.
Find the total distance traveled by the dog after (26pi)/2 seconds.
hope this would verify confusion
- Joined
- Feb 4, 2004
- Messages
- 16,582
If we have no ending time, we only know that we're counting his distance starting at t = 13pi seconds. Since we have no ending time, we have absolutely no way of knowing how far he'd run after 13pi seconds, because we don't know how long he ran.
I'm sorry if this upsets you, but we're not trying to be difficult. You're asking us to find the distance he ran, but aren't telling us how long he ran. Since "distance equals rate times time", and you've only given us the rate and no ending time, there is no way to determine the distance.
So, yes, reposting the exact same exercise, without providing the missing information, does indeed "verify" the confusion. :?
Eliz.
I'm sorry if this upsets you, but we're not trying to be difficult. You're asking us to find the distance he ran, but aren't telling us how long he ran. Since "distance equals rate times time", and you've only given us the rate and no ending time, there is no way to determine the distance.
So, yes, reposting the exact same exercise, without providing the missing information, does indeed "verify" the confusion. :?
Eliz.
- Joined
- Apr 12, 2005
- Messages
- 11,339
[0,pi/2] ==> 1
[pi/2, pi] ==> 1
[pi, 3pi/2] ==> -1
[3pi/2, 2pi] ==> -1
Summary: [0,2pi] ==> 1+1-1-1 = 0
Conclusion: [0,12pi] ==> 0
One more pi and we have the displacement.
For total travelled, [0,12pi] ==> 24
One more pi and we have the travel total.
That's one crazy dog.
Writing a clear question is a very important business. Simply insisting that a question it is clear, when folks who know better tell you it isn't, doesn't really help.
[pi/2, pi] ==> 1
[pi, 3pi/2] ==> -1
[3pi/2, 2pi] ==> -1
Summary: [0,2pi] ==> 1+1-1-1 = 0
Conclusion: [0,12pi] ==> 0
One more pi and we have the displacement.
For total travelled, [0,12pi] ==> 24
One more pi and we have the travel total.
That's one crazy dog.
Writing a clear question is a very important business. Simply insisting that a question it is clear, when folks who know better tell you it isn't, doesn't really help.