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I What is instantaneous acceleration?

  1. May 8, 2017 #1
    How their can be instantaneous acceleration, its impossible to have change in velocity at a particular position(instant), we can have velcoity or speed at a particular point but how can we have change in velocity at a particular instant?
     
  2. jcsd
  3. May 8, 2017 #2

    andrewkirk

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    We don't.

    Acceleration is simply the derivative of velocity with respect to time. Spend some time pondering the definition of derivative as a limit as ##\delta t\to 0##, and how it applies to this particular case, and you'll see how it works.
     
  4. May 8, 2017 #3
    You mean Δt→0
     
  5. May 8, 2017 #4

    Ssnow

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    Hi, from your velocity function ##v(t)## respect the time ##t## you can define the instantaneous acceleration in ##t=t_{0}## by the derivative:

    ##a(t_{0})=\lim_{\Delta t \rightarrow 0}\frac{v(t_{0}+\Delta t)-v(t_{0})}{\Delta t}##

    Ssnow
     
  6. May 8, 2017 #5

    andrewkirk

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    No I don't.
     
  7. May 8, 2017 #6
    @Ssnow
     
    Last edited: May 8, 2017
  8. May 8, 2017 #7
    I think we defined instantaneous acceleration mainly to use its vector property so that we can determine in which direction velcoity is increasing and its magnitude will be the change in velocity at a very small interval(and we say it as change in velocity at an instant or acceleration at an instant), therefore we never use scalar version or we didn't defined scalar version of acceleration.
    Its just my attempt to answer this question.
     
  9. May 8, 2017 #8

    jbriggs444

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    If we can define instantaneous velocity as the instantaneous rate of change of position with respect to time then how is it problematic to define instantaneous acceleration as the instantaneous rate of change of velocity with respect to time?
     
  10. May 8, 2017 #9
    when you first get in your car, a=0. You turn the key, a=0. You start to move, a=10 (pick any unit you want) then a few seconds later now the wheels are going faster a=40, then the wheels can't really go any faster so a=20, and at top speed when you can't get any faster a=0. It's useful to measure acceleration as an average, e.g. from start to a top speed of 60mph, we might say the car went from 0 to 60 in so many seconds. But when breaking down the motion into separate instances, we have different accelerations. This is the concept of instantaneous acceleration, i.e. the acceleration at this or that moment, as opposed to an average acceleration.
     
  11. May 8, 2017 #10
    So the final definition becomes,

    1. instantaneous velcity is the velocity of the particle at an instant{its completely logical because we can find the velcity of a particle at a particular instant(time)}
    2. Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)
    As you said that whats the problem in defining this way, i didn't said that we can't define acceleration as rate of change of velocity(i think this definition is good for average acceleration but not for instantaneous acceleration as for above reasons)
     
  12. May 8, 2017 #11
    thats the simple physics definition. If you then have an issue with the math... v=dx/dt, a=dv/dt, they are the same mathematical objects: a derivative w.r.t a variable t; where x, v, and a are the vector quantities displacement, velocity and acc respectively.
     
  13. May 8, 2017 #12
    If you replace in 2. "rate of change of velocity of a particle" with "acceleration" .OR. replace in 1. "velocity of" with "rate of change of displacement of". Do you still have the same conceptual problem?
     
  14. May 8, 2017 #13

    A.T.

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    Note how the red part is missing in your question.

    Seems like your problem is with math, not with physics:
    https://en.wikipedia.org/wiki/Differential_calculus

    And your logic makes no sense to me. Acceleration is a derivative of velocity, just like velocity is a derivative of position. Both have a instantaneous value at every time point.
     
  15. May 8, 2017 #14
    How can we have a change in velcity at an instant(or acceleration at an instant)
     
  16. May 8, 2017 #15

    A.T.

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    See post #13 again, I edited it.
     
  17. May 8, 2017 #16
    Do you mean that accelaration is the velocity at a instant of time and velocity is the position of a particle at a instant of time.
     
  18. May 8, 2017 #17
    same way you can have change in position at an instant.
    no. you need to learn calculus, which will define what an instantaneous rate of change is.
     
  19. May 8, 2017 #18

    jbriggs444

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    How, experimentally, will you find the velocity of a particle at a particular instant?

    Mathematically, we can define it -- no problem.
     
  20. May 8, 2017 #19
    By drawing a tangent at that instant
     
  21. May 8, 2017 #20
    impossible
     
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