Integral of Momentum - Questions Answered

[Dominique]

Hi,

QUESTION 1
??=dF/dt
F =ma=dp/dt (force)
p =mv=d?/dt (linear momentum)
? =mx

A) Is there a quantity defined as the mass times the position or as the integral over time or the the linear momentum?
B) Is there a quantity defined as the derivative wr to time of the force?


QUESTION 2
?? = intergal over time of power
P =(mv^2)/2t (power)
K =(mv^2)/2 (kinetic energy)
? = dK/dt

A) Is there a quantity defined as the derivative over time of energy?
B) Is there a quantity defined as the integral over time or the power?


Thank you very much for your help!

 

[kuruman]

You can define any quantity you want ... but is it useful?

For example (I am making this up) the quantity $mx$ could find use in athletic competition where strong athletes pull vehicles over a distance. Their rating of how strong they are could be cast in terms of the product $mx$ for comparative purposes. Not a very useful quantity to define.

Question 2 requires nothing to be made up artificially. The time-rate of change of energy is power and of course the integral of power over time is energy or mechanical work. Power is a very useful quantity and is used extensively as you know to characterize anything that has to do with the use of electricity, heat and mechanical work.