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Average Power
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 Pₐ in terms of variables: the mass M, the final speed V, and the distance d.
Pₐ=Pₐ(M,V,d) ?
Ignore energy lost due to friction and air resistance.
Derive a formula for average power Pₐ in terms of variables: the mass M, the final speed V, and the distance d.
Pₐ=Pₐ(M,V,d) ?
Solution:
Pₐ=W/t
K-Kₒ=W
Kₒ=0
K=½MV²
Pₐ=½MV²/t
V=at
d=½at²=
½Vt
t=2d/V
Pₐ=½MV²/(2d/V)
= ¼MV³/d
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