Why total time taken s₁/v₁ + s₂/v₂ + s₃/v₃ in average speed?

  • Thread starter Indranil
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  • #1
Indranil
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Homework Statement


As we know the Average speed = Total distance / Total time but why in the case below
Distance traveled = s₁ + s₂ + s₃ and total time taken = s₁/v₁ + s₂/v₂ + s₃/v₃ How is it possible? so, altogether
Vav = s₁ + s₂ + s₃ / ( s₁/v₁ + s₂/v₂ + s₃/v₃)


Homework Equations




The Attempt at a Solution


I only know (Average speed = Total distance / Total time)
 

Answers and Replies

  • #2
Doc Al
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The total time is the sum of the times for each segment, which you can calculate (as shown) given the speed and distance in each segment.
 
  • #3
Stephen Tashi
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How is it possible?
What do you mean by "it"? What question does the problem ask?

so, altogether
Vav = s₁ + s₂ + s₃ / ( s₁/v₁ + s₂/v₂ + s₃/v₃)
Perhap you meant ##V_{av} = (s_1 + s_2 + s_3)/ ( s_1/v_1 + s_2/v_2 + s_3/v_3) ##.

You didn't explain the variables. My guess is that the problem states that an object travels distance ##s_i## at average velocity ##v_i## for ##i =1,2,3##.
 
  • #4
Indranil
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What do you mean by "it"? What question does the problem ask?


Perhap you meant ##V_{av} = (s_1 + s_2 + s_3)/ ( s_1/v_1 + s_2/v_2 + s_3/v_3) ##.

You didn't explain the variables. My guess is that the problem states that an object travels distance ##s_i## at average velocity ##v_i## for ##i =1,2,3##.
It means total time taken 's₁/v₁ + s₂/v₂ + s₃/v₃' How is it possible?
 
  • #5
Indranil
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The total time is the sum of the times for each segment, which you can calculate (as shown) given the speed and distance in each segment.
Could you get your point a little bit easier, please?
 
  • #6
Doc Al
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Could you get your point a little bit easier, please?
If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?
 
  • #7
Indranil
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If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?
That's what I want to learn. Please explain
 
  • #8
Doc Al
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That's what I want to learn. Please explain
How about this: Distance = Speed X Time.

Solve for time.
 
  • #9
Indranil
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How about this: Distance = Speed X Time.

Solve for time.
Time = distance / speed
 
  • #10
Indranil
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If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?
Now I got it what you mean.
 
  • #11
Indranil
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How about this: Distance = Speed X Time.

Solve for time.
Now what about this equation Vav = 2v₁v₂ / (v₁ + v₂) Could you simplify it please?
 
  • #12
Doc Al
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Now what about this equation Vav = 2v₁v₂ / (v₁ + v₂) Could you simplify it please?
That's a very specialized formula. Consider something moving from point A to point B at speed v1 and then back to A at speed v2. Now can you figure it out?
 
  • #13
Indranil
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That's a very specialized formula. Consider something moving from point A to point B at speed v1 and then back to A at speed v2. Now can you figure it out?
Still, I don't understand what you mean. get your point a little bit easier. how do we get '2v₁v₂' in the place of distance and why do we add '(v₁ + v₂)' in the place of time?
 
  • #14
jbriggs444
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Still, I don't understand what you mean. get your point a little bit easier. how do we get '2v₁v₂' in the place of distance and why do we add '(v₁ + v₂)' in the place of time?
Try following @Doc Al's suggestion. Let d be the distance from point A to point B. Write down a formula for the average velocity: total distance divided by total time. Show us that formula.
 
  • #15
Indranil
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Try following @Doc Al's suggestion. Let d be the distance from point A to point B. Write down a formula for the average velocity: total distance divided by total time. Show us that formula.
Vavg = d / t
 
  • #16
jbriggs444
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Vavg = d / t
First, a round trip does not have distance = d. Now write that "t" in terms of d, v1 and v2
 
  • #17
Indranil
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First, a round trip does not have distance = d. Now write that "t" in terms of d, v1 and v2
like this equeation Vavg = t v₁v₂ / t?
 
  • #18
jbriggs444
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like this equeation Vavg = t v₁v₂ / t?
That equation makes no sense. If points A and B are distance d apart, how much time does it take to get from A to B at speed v1?
 
  • #19
Indranil
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That equation makes no sense. If points A and B are distance d apart, how much time does it take to get from A to B at speed v1?
I think t1 time required
 
  • #20
jbriggs444
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I think t1 time required
One more try and then I'm out. Please write a formula for t1 that uses only d and v1
 
  • #21
Indranil
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One more try and then I'm out. Please write a formula for t1 that uses only d and v1
Yes t1 = d / v1
 
  • #22
jbriggs444
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Yes t1 = d / v1
OK. Now repeat for t2, the time for the return trip.
Then write down a formula for the total time taken for the round trip.
Finally, write down a formula for the average velocity over the round trip using only d, v1 and v2.
 
  • #23
Indranil
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OK. Now repeat for t2, the time for the return trip.
Then write down a formula for the total time taken for the round trip.
Finally, write down a formula for the average velocity over the round trip using only d, v1 and v2.
t1 + t2 = d / v1 + d / v2, t = d (v1 + v2) / v1v2, Vavg = d / t = d / d(v1 + v2) / v1v2 = v1v2 / v1 + v2 [ but the equeation is 2v1v2 / v1 + v2] Could you check my calculation please?
 
  • #24
Stephen Tashi
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It means total time taken 's₁/v₁ + s₂/v₂ + s₃/v₃' How is it possible?

Total time to go distance (s1 + s2 + s3) = time to go s1 + time to go s2 + time to go s3
time to go distance s1 = s1/v1 etc.
 
  • #25
Doc Al
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t1 + t2 = d / v1 + d / v2,
This is correct, but the rest of your work is hard to understand. Now write a general expression for the average speed, making use of this expression for the total time.
 
  • #26
jbriggs444
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t1 + t2 = d / v1 + d / v2, t = d (v1 + v2) / v1v2, Vavg = d / t = d / d(v1 + v2) / v1v2 = v1v2 / v1 + v2 [ but the equeation is 2v1v2 / v1 + v2] Could you check my calculation please?
ttot
= t1 + t2. Yes.
= d/v1 + d/v2. Yes.
= d(v1 + v2) / (v1v2). Where did this come from?

Vavg = d/t Is incorrect. The round trip distance is not given by d.
 
  • #27
Indranil
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This is correct, but the rest of your work is hard to understand. Now write a general expression for the average speed, making use of this expression for the total time.
Vavg = d / t. as t =
ttot
= t1 + t2. Yes.
= d/v1 + d/v2. Yes.
= d(v1 + v2) / (v1v2). Where did this come from?

Vavg = d/t Is incorrect. The round trip distance is not given by d.[/sub][/sub]
d(v1 + v2 / (v1v2.) this comes from the adition of (d / v1 + d / v2)
 
  • #28
jbriggs444
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Vavg = d / t.
No, it isn't.

d(v1 + v2) / (v1v2.) this comes from the adition of (d / v1 + d / v2)
If you skip past the steps where you multiply the first fraction by v2/v2 and the second fraction by v1/v1. combine the terms and factor out the d then yes, that sum follows.

Now what is the round trip distance?
 
  • #29
Doc Al
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Vavg = d / t.
You want Vave = Total distance / total time.

Total distance is not equal to 'd'.
 
  • #30
Indranil
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You want Vave = Total distance / total time.

Total distance is not equal to 'd'.
Vavg = d1 + d2 / t1 + t2?
 
  • #31
jbriggs444
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Vavg = d1 + d2 / t1 + t2?
What are d1 and d2? We have two points, A and B with distance d between them.

[Note that parentheses matter]
 
  • #32
Indranil
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What are d1 and d2? We have two points, A and B with distance d between them.

[Note that parentheses matter]
Vavg = s / t ?
 
  • #33
jbriggs444
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Vavg = s / t ?
What's s? We have two points A and B with distance d between them.
 
  • #34
Indranil
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What's s? We have two points A and B with distance d between them.
could you mention the equation, please?
 
  • #35
jbriggs444
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could you mention the equation, please?
No. That's your job.
 
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