# PHYSICS - formula?

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Here is one of my questions from my physics study. It tells me the answer (35 J), but how do I find that answer? I would appreciate a formula or step by step calculation. Thanks! :)

A 30 kg kid on rollerskates is moving 1 m/s. His brother pushes him with a force of 5 N. What will be his kinetic energy after his brother pushes him 4.0 m? (35 J)

• PHYSICS - formula? -

What acceleration does the pushing impart?
F=ma
5=30a
a = 1/6

How long does it take to go 4m, starting at 1m/s?
s = Vo t + 1/2 at^2
4 = t + 1/2 * 1/6 t^2
t^2 + 12t - 48 = 0
t = 4

What's the speed after 4 seconds?
v = Vo+at
= 1 + 1/6 * 4
= 5/3

What's the KE then?
KE = 1/2 mv^2
= 1/2 (30)(5/3)^2
= 15*25/9
= 125/3

Hmmm. better check my math.

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