Question

Derive the 1st equation of motion using dimensional analysis.

Answer 1

Answer:

Explanation:

he dimension of this equation is zero,

PROOF:

remember that, for distance we use capital “L” and for time we use capital “T” only in dimensions so we have equation

vf=vi+a*t,

velocity has dimension LT^-1 because the formula of velocity is

V=S/T, here S is displacement and T is time,

V=L/T,

V=LT^-1,

acceleration has dimension LT^-2 because the formula of acceleration is

a=v/t, here v is velocity and t is time,

a=LT^-1/T,

a=LT^-1*T^-1,

a=LT^-2

by putting these dimension in above equation we get,

LT^-1=LT^-1+LT^-2*T,

LT^-1=LT^-1+LT^-1,

LT^-1=2*LT^-2

and every number is dimension less

so we have,

LT^-1=LT^-1,

=0 proved................

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