Question

derive the formula: S=ut+1/2atsq.,where the symbols have usual meanings

Answer 1

Terminology : a = acceleration, v = final velocity , u = intial velocity, t = time.

From the definition of Acceleration ,

a = v - u / t.

Now, Transposing t to Left hand side.

at = v - u

Transpose -u to Left hand side.

at + u = v.

Interchanging the sides of the equation,

v = u + at.

Now, We have two velocities " u " & " v " .

Average velocity = u + v /2 .

We know that,
Velocity = Distance / Time

Distance = Velocity * Time

s = ( u + v) t / 2

Substitute v = u + at.

s = ( u + u + at ) t /2

s = ( 2u + at) t /2

s = ut + 1/2 at² .

Hence proved !