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rcgldr

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p = power (constant)

a = acceleration

v = velocity

x = position

t = time

f = force

Assume an object is initially at rest, at position zero and time zero:

v

_{0}= 0

x

_{0}= 0

t

_{0}= 0

f = m a

p = f v

f = p / v

first step

a = f / m = dv/dt = p / (m v)

v dv = (p/m) dt

1/2 v

^{2}= (p/m) t

[tex] v = \frac{dx}{dt} = \sqrt {\frac{2\ p\ t}{m}} [/tex]

This is continued to find x as a function of t, then t as a function of x

Then determine f(x) = p / v(x)

and finally show that work done is

[tex]p\ t_1 = \int_0^{x_1} f(x) dx [/tex]