Question

Derive equation for position velocity relation

Answer 1

equation for position velocity realtion consider graph given above..
we know that distance travelled s by a body in time t is given by the area underline AB which is area of trapezium OABC
so we have
distance travelled =s = are of trapezium OABC
s=(sum of parallel sides )×h/2
=(OA+CB)×OC/2
since OA+CB= u+band OC=t
than we get
s=(u+v)t/2...................(eq.1)
from velocity time relation
t=v-u/a
substituting the value of t in equation 1 we get
s=(u+v)/2(v-u)/2

or we have..
v^2 = u^2 + 2as
which is the equation of position velocity realtion
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