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How does a= d/t and f/m ?

  1. Dec 11, 2012 #1
    1. The problem statement, all variables and given/known data

    If a = d/t how can it also = f/m ? I cant see a common unit between the two equations.

    In the first one if I covered 50m in 20 s I'd be accelearting at a rate of 5m per 2s or would it be 5m per 2 s^2.

    So how does then become force * mass ? what would force * mass become as a unit ? would it newtons per kilo ? and how does this then become meters per second ?

    2. Relevant equations



    3. The attempt at a solution

    whoa...totally unsure where to start in terms of a solution.
     
  2. jcsd
  3. Dec 11, 2012 #2

    ehild

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    Distance covered over time is (average) speed, not acceleration. If you cover 50 m in 20 s your speed is 2.5 m/s.
    Acceleration is change of velocity during unit time. If your velocity increases to 3 m/s from 2 m/s in 5 s then your acceleration is a=1/5 =0.2 m/s2.

    ehild
     
  4. Dec 11, 2012 #3
    thanks for that ...I'm still unsure though how a = change in velocity during unit time to becoming a = f/m...I cant quite understand the link here or see the common unit to convert one to the other
     
  5. Dec 11, 2012 #4
    It may because you aren't examining the units closely enough if you are simply going off a dimensional comparison. In metric acceleration has units of m/s/s, mass is in kg, and force in Newtons. In english units acceleration is in ft/s/s,mass is in slugs and force is in lbf(pounds force). If you want to see the equivalence between both units you have to remember that force regardless of system is a derived unit meaning it comes as a compounding of basic units. One Newton is defined as one kg*m/s/s. Similarly pound-force is equivalent to one slug*ft/s/s. If you plug these units into the above equations you should find that the units work out in both cases because mass cancels on the force side. In general: acceleration=LT^-2 and force=MLT^-2.
     
  6. Dec 11, 2012 #5
    Acceleration is defined as the amount by which the speed (velocity) changes in a unit of time. It tells you the rate of change of speed, for instance g = 9.8 m/s2 tells us that the speed of the object will change with 9.8 m/s for each elapsed second. this definition is given in the kinematics chapter of a physics handbook. Here acceleration is calculated by looking at the change in speed of the object

    The second time one meets the acceleration is when the question is investigated - How do the motion of an object change (its acceleration) if a force F is applied to it and its inertia (mass) is m. Here we calculated the acceleration from its mass and the (net) applied force acting on it. So they are two different ways to get the same quantity, either from a kinematic or a dynamic viewpoint.
     
  7. Dec 11, 2012 #6
    d/t is not equal to acceleration, that's velocity. In terms of displacement, acceleration is (d^2/dt^2)d. You could also say it's equal to v/t.
    There's no need to "convert." The standard units of acceleration are m/s^2. If you work out the units for f/m, it comes out to be m/s^2. You can also work out the units for v/t or (d^2/dt^2)d and it comes out to be m/s^2.

    I should mention that the d in (d^2/dt^2) is a differential, and not displacement.
     
  8. Dec 11, 2012 #7

    ehild

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    Observing the motion of objects, Newton found out that the force causes acceleration, and the acceleration of an object is proportional to the force exerted on it, and inversely proportional to the mass of the object: Force is equal to mass times acceleration, F=ma. The unit of force is called "newton", it is the same unit as kg m /s2.

    ehild
     
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