Question

how to derive the second equation of motion

Answer 1

S=ut+12at2S=ut+12at2 [where, u is the initial velocity, a is the acceleration and t is the time interval]This Equation simply finds a relation between distance travelled by a particle (classically) under uniform acceleration.Follow the statement I said in italics. In order to find the distance covered by the particle, we need to find some equations to start with. Right??So let's see what pieces of information (bundles of equations) do we have with us, initially.We have, a very primary equation with us, dSdt=v…dSdt=v…(I)(I)(Considering motion in a straight line only)

Answer 2

 Second equation of motion:
s = ut + 1/2 at^2

sol.
Let the distance travelled by the body be “s”.
We know that
Distance = Average velocity X Time

Also, Average velocity = (u+v)/2

.: Distance (t) = (u+v)/2 X t …….eq.(1)

Again we know that:
v = u + at
substituting this value of “v” in eq.(2), we get

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

or s = ut +1/2 at^2

so hi hope it will help you 

regards