Monday, January 2, 2017

New Year Math Problems: (2016! mod 2017) - (2017! mod 2016)=? (2016! mod 2017) - (2017! mod 2018)=?

New Year Math Problems: (2016! mod 2017) - (2017! mod 2016)=?
(2016! mod 2017) - (2017! mod 2018)=?

Saturday, October 1, 2016

Physics Problem - What is the Average Power Output of an Engine?

What is the average power output of an engine when a car of mass M accelerates uniformly (a=const) from rest to a final speed V over a distance d on flat, level ground? Ignore energy lost due to friction and air resistance. Derive a formula for average power P in terms of variables: the mass M, the final speed V, and the distance d.
P
=P(M,V,d) ?

Solution:
Pₐ=W/t
K-Kₒ=W
Kₒ=0
KMV²
PₐMV²/t
V=at
d=½at²= ½Vt
t=2d/V


PₐMV²/(2d/V) = ¼MV³/d