Answer to Question #147492 in Mechanics | Relativity for Afraid

Question #147492
What is second equation of motion.
1
Expert's answer
2020-12-02T07:34:06-0500

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

S=V(initial)×\times t+ a×t22\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+ a×t22\frac{a \times t^2}{2}

Derivation We know that Velocity = DisplacementTime\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 =Initialvelocity+Finalvelocity2\frac{Initial velocity + Final velocity}{2}×\times Time

S=V(initial)+V(final)2\frac{V(initial)+V(final)}{2}×\timest, V(final)- final velocity.

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

Putting value of Vf in this equation:

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

S=(V(initial)+a×t2\frac{a \times t}{2})×\timest

S=V(initial)×\times t+a×t22\frac{a \times t^2}{2} . So that is answer!

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