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Old Aug 2nd 2017, 11:05 AM   #1
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Issues with Kinetic Energy Formulae

we know that energy=work done=F*s

f=ma

therefore, e=ma*s

if initial velocity is 0,acceleration is final velocity divided by the time taken

therefore,e=m*v/t*s

velocity is distance pet unit time

therefore,e=m*(s*s/t*t)
e=m*(s^2/t^2)
e=m*v^2

how is this possible when we know that kinetic energy of a body is
1/2mv^2 ??
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Old Aug 2nd 2017, 11:19 AM   #2
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velocity is distance per unit time
yes but,
you are applying the final velocity to the entire time period
you should be using the average velocity!
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Old Aug 2nd 2017, 11:37 AM   #3
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Just to be clear, you claim that s/t = v, but that's true only of velocity is constant. It's not in this case - and as Woody says you should use the average velocity, so s/t = v/2. You can see thus from the basic equation of motion - for initial velocity = 0:

s = (1/2) a t^2, or

s = (1/2) (v/t) t^2 = (1/2) (vt).

Hence s/t = v/2.
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Old Aug 2nd 2017, 01:14 PM   #4
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Originally Posted by RishabhChhajer View Post
we know that energy=work done=F*s

f=ma

therefore, e=ma*s

if initial velocity is 0,acceleration is final velocity divided by the time taken

therefore,e=m*v/t*s

velocity is distance pet unit time

therefore,e=m*(s*s/t*t)
e=m*(s^2/t^2)
e=m*v^2

how is this possible when we know that kinetic energy of a body is
1/2mv^2 ??
The work done by a force exerted by, say, your hand, doesn't always change the speed and thus the kinetic energy. For example, let's say that you're moving a book across a table by pushing it from point A to point B where the speed is constant and in a straight line, i.e. force is in direction of motion. Then the work done by you is Force x distance. The energy that you expended goes into thermal energy of the block and the table. There is no kinetic energy change because that involves the total force and in this example we ignored the force of friction because we were only interested in the energy that you expended so we could determine how much of that energy went into thermal motion.

I just noticed that I never created a webpage to describe this. I've got my work cut out for me I see?
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