Question

derive all the equations of motion and explain how they formed properly first and right answer be marked as brain list answer please answer it fast

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]

This is the first equation of motion


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]

v̅ = ½(v + v0) [4]

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

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

Explanation:

There are three equations of motion that can be used to derive components such as displacement(s), velocity (initial and final), time(t) and acceleration(a). The following are the three equation of motion: First Equation of Motion : v=u+at. Second Equation of Motion : s=ut+\frac{1}{2}at^2.