derieve the formula for kinetic energy of a particle having mass m and velocity v using dimensional analysis
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Explanation:
m = mass of body
f = force of body
a = acceleration of body
v = velocity of the body
using eq.
vsq.-usq. = 2as
vsq.- 0 = 2as
a = vsq./ 2s. ..... (1)
f = ma using 1st
f = m (vsq./ 2s )... (2)
work force× distance using 2nd
w = m (vsq./ 2s )× s
w = 1/2 mvsq.
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Derivation :
Suppose mass of a particle =m, velocity=v
u =0m/s
F=ma
s= v^2 -u^2/2a
on substitution of value, we get
Work = Force*displacement
= ma*v^2/2a
= 1/2 mv^2
Work done on object to set it into motion is conserved in form of kinetic energy in it.
KE = 1/2 mv^2
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