Question

5. Deduce the following equations of motion i
s = ut + (1/2)at? ii) v2 = u? + 2as​

Answer 1

Explanation:

Deducing the 2nd equation of motion

distance = average velocity x time. ( only in case of uniformly accelerated one dimensional motion)

=> distance = ( u + v) /2 x t

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

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

=> s =( 2ut + at^2 )/2

=> s = ut + (1/2)at^2

Hence proved.

Deducing the 3rd equation of motion

distance = average velocity x time

=> s = ( u + v) /2 x t

=> s = ( v + u) /2 x ( v - u) /a

=> s = ( v + u) (v - u) /2a

=> 2as = v^2 - u^2

=> v^2 - u^2 = 2as

Hence proved.

Basic formulas used in the deductions :

1. avg. velocity =( initial velocity + final velocity) /2

2. v = u + at ( used in the first deduction, according to the 1st equation of motion)

3. t = ( v - u) /a ( used in the second deduction, according to the 1st of motion by rearranging the variables)