1. show how the alternative definition of power, found in your book, can be derived by substituting the definitions of work and speed into the standard definition of power, p = w / delta t. 2. a real spring does not oscillate forever. instead, it eventually comes to a stop. does this violate the law of conservation of energy? explain why or why not.

1) Star from the definition of power:

P = work/ time = W / Δt

We know that work is given by force times displacement:
 W = F · Δd
Substituting in our formula: 
P = F · Δd / Δt

But we know by definition that Δd / Δt = velocity, therefore we can write:
P = F · v
which is the alternative formula saying that Power is equal to Force times Velocity

2) No, it is not a violation of the Law of conservation of energy because as the spring slows down, the kinetic energy is transformed into potential energy and their sum stays constant.

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