Question

show the derivation of second equation of motion

Answer 1

This is the easiest of the three equations to derive using algebra. Start from the definition of acceleration.

a = ΔvΔt

Expand Δv to v − v0 and condense Δt to t.

a = v − v0t

Then solve for v as a function of t.

v = v0 + at [1]

Start with the definition of velocity.

v̅ = ΔsΔt

Expand Δs to s − s0 and condense Δt to t.

v̅ = s − s0t

Solve for position.

s = s0 + v̅t [a]

Substitute the first equation of motion [1] into this equation [4] and simplify with the intent of eliminatingv.

v̅ = ½[(v0 + at) + v0]  v̅ = ½(2v0 + at)  v̅ = v0 + ½at [b]

Now substitute [b] into [a] to eliminate v̅ [vee bar].

s = s0 + (v0 + ½at)t

And finally, solve for s as a function of t.

s = s0 + v0t + ½at2 [2]

Answer 2

one is derived by simple method and other is derived by graphical method.
hope it helps
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