To find the particle's velocity

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SUMMARY

The discussion centers on calculating the velocity of a particle moving along the x-axis with a time-dependent acceleration defined by the equation f = f°(1 - t/T), where f° and T are constants. The particle starts with zero velocity at t = 0, and the solution for its velocity at the moment when f = 0 is determined to be f°T/2. Participants emphasize the importance of understanding integration limits and the distinction between average and instantaneous velocity in solving the problem.

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Homework Statement


A particle is moving along the x-axis has acceleration 'f' at time ' t ' given by :
f= f°(1- t /T) where f° and T are constants .The particle at t = 0 has zero velocity . In the time interval between t= 0 and the instant when f= 0 ,the particle's velocity is ?

Homework Equations


a= dv/dt
Where 'a' = acceleration
'v' = velocity
' t' = time

The Attempt at a Solution


I'm totally confused. I am not getting any idea of how to solve this problem. Please help. The answer is f°T/2[/B]
 
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Nikhil faraday said:

Homework Statement


A particle is moving along the x-axis has acceleration 'f' at time ' t ' given by :
f= f°(1- t /T) where f° and T are constants .The particle at t = 0 has zero velocity . In the time interval between t= 0 and the instant when f= 0 ,the particle's velocity is ?

Homework Equations


a= dv/dt
Where 'a' = acceleration
'v' = velocity
' t' = time

The Attempt at a Solution


I'm totally confused. I am not getting any idea of how to solve this problem. Please help. The answer is f°T/2[/B]

If ##a = dv/dt##, then what is ##v## in terms of ##a##? Remember that, in this case, ##a## is not constant, it is changing over time.
 
I'm still not getting it. I have done the integration but not sure what, how to take limits.
 
Is the problem stated exactly as it was given to you? If the particle accelerates during the specified time interval then it's velocity over that interval won't be a constant value. Perhaps they are looking for the average velocity? Or average speed?
 
gneill said:
Is the problem stated exactly as it was given to you? If the particle accelerates during the specified time interval then it's velocity over that interval won't be a constant value. Perhaps they are looking for the average velocity?

Or ##v## as a function of ##t## over that interval?
 
PeroK said:
Or ##v## as a function of ##t## over that interval?
The given solution is apparently a constant. So it makes me wonder about what might be considered a constant for an interval of time where the velocity and position are changing. The only thing that springs to mind is the average velocity for that time period.
 
This is the question! the answer is option III.
 

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Nikhil faraday said:
This is the question! the answer is option III.

My approach would be to solve the problem first. Re the limits of integration: when is ##f = 0##?

This is why you must show us, or at least tell us, what you have tried. How do we know you have tried integrating? Your original post said you were "totally confused", which doesn't appear to be the case!
 
Nikhil faraday said:
This is the question! the answer is option III.
The image is fuzzy. I can't make out the subscript on V :
upload_2016-11-1_10-31-22.png


What is that subscript?
 
  • #10
PeroK said:
My approach would be to solve the problem first. Re the limits of integration: when is ##f = 0##?

This is why you must show us, or at least tell us, what you have tried. How do we know you have tried integrating? Your original post said you were "totally confused", which doesn't appear to be the case!

PS if you find the velocity at time ##t##, then all will be clear!
 
  • #11
Gneill ,the subscript on v is just 'x' indicating velocity in x direction.
 
  • #12
Thank you all for all your help ! I don't think I am made for physics. I can't even solve problems like this. It is good that I am in my beginning of my course ,I can leave it it will be good for me.
 
  • #13
Nikhil faraday said:
Thank you all for all your help ! I don't think I am made for physics. I can't even solve problems like this. It is good that I am in my beginning of my course ,I can leave it it will be good for me.
I think that the question was poorly phrased, making it hard to understand what they were really looking for. So for a beginner it would be understandably confusing if you don't have all the concepts sorted out and firmly understood without any doubts to make things harder.

Stick with it. As long as you have the necessary math things should get better once you've become familiar with the basics and the way physics problems are phrased and presented to convey what concepts are important for solving them. You'll start to recognize key words and phases that imply what's intended and how best to approach the problem.
 
  • #14
Thank you . I will try my best to solve it.
Tomorrow , it's night here
 
  • #15
Finally got it☺☺! I was making the mistake in doing the integration. Nothing make you more happy than doing a good physics problem.
 

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