Answer to Question #147492 in Mechanics | Relativity for Afraid

Question

What is second equation of motion.

Answer 1

The second equation of motion gives the displacement of an object under constant acceleration:

S=V(initial)$\times$ t+ $\frac{a \times t^2}{2}$ ,

S - travelled distance,

V(initial) - initial velocity,

t - spent time and

a - acceleration.

Let`s to proof it:

We saw above the Second Equation of Motion

S=V(initial)$\times$ t+ $\frac{a \times t^2}{2}$

Derivation We know that Velocity = $\frac{Displacement}{Time}$  If Velocity is not constant (i.e. Velocity keeps on increasing or decreasing) We can also take Average Velocity in place of Velocity.

So our formula becomes Displacement = Average Velocity $\times$ Time 

Displacement =$\frac{Initial velocity + Final velocity}{2}$$\times$ Time

S=$\frac{V(initial)+V(final)}{2}$$\times$t, V(final)- final velocity.

From first equation of motion, we know that: V(final)=V(initial)+a$\times$t, a - acceleration.

Putting value of V_f in this equation:

S=$\frac{V(initial)+(V(initial)+a \times t)}{2} \times t$,

S=(V(initial)+$\frac{a \times t}{2}$)$\times$t

S=V(initial)$\times$ t+$\frac{a \times t^2}{2}$ . So that is answer!