5 Mathematically prove that the distance [s] travelled by an object is the average mean of initial velocity[u] and final - Science - Motion

Question

5 Mathematically prove that the distance [s] travelled by an object
is the average
mean of initial velocity[u] and final velocity [v] having constant
acceleration in
the direction of motion in a straight line

Anshu Agrawal · Accepted Answer

Dear student,
V = U + at  V² - U²   =  2as  => S  =  (V² - U² )/2a  using x² - y² = (x + y)(x - y)  => S = (V + U)(V - U)/2a  V = U + at    => V - U = at  = S = (V + U)(at)/2a  => S=  (V + U)( t)/2  => S =  ( ( V + U)/2 ) × t  ( V + U)/2   = mean of initial velocity[u] and final velocity [v]

Regards

5.Mathematically prove that the distance [s] travelled by an object is the average mean of initial velocity[u] and final velocity [v] having constant acceleration in the direction of motion in a straight line.

5.Mathematically prove that the distance [s] travelled by an object is the average
mean of initial velocity[u] and final velocity [v] having constant acceleration in
the direction of motion in a straight line.