# Equations of Motion

##
Equations of Motion

Initial velocity = u

Final velocity = v

Acceleration = a

Ela[sed time = t

Distance = d

**Formula:**

1) s = vt

2) v = u + at

3) v^{2} = u^{2} + 2as

4) s = ut + ^{1}/_{2} at^{2}

If an object has no acceleration hen there is no change in its velocity. Then the initial velocity and the final velocity will be equal i.e (u = v). Therefore the distance covered will be, s = vt.

If there is uniform acceleration, the final velocity is: v = u + at

This equation shows that the velocity is changing with time. Therefore to calculate the travelled distance, velocity at any instant is to be multiplied by the time of that instant and then the total distance, for the elapsed time, determined. For this type of calculation we have to know a special type of mathematics (called calculus), here we will solve it without this mathematics. This will be possible since we are concerned only with uniform acceleration. If it is not uniform acceleration, it would not be possible.

Since the velocity is changing is changing every moment hence we cannot write the equation **s = vt** but if we consider an average velocity V then we can write

s = Vt

It means that to calculate the distance travelled we have to find only the average velocity. For uniform acceleration it is easy to the find average velocity. If anything increases uniformly then its average value is exactly equal to its mean value. In the other words if anything increases uniformly then the arithmetic mean of its initial and final values represents its average value. i.e,

V = (u+v) ÷ 2

= {u + (u+at)} ÷ 2

= u + ^{1}/_{2} at

Therefore, the travelled distance is,

s = Vt

= ( u + ^{1}/_{2 }a)t

s = ut + ^{1}/_{2} at^{2}

In all, the equations of motion we have already deduced the time t is present. We can deduce another equation in which t is absent.

Such as: v^{2} = u^{2} + 2as

Although this equation looks like another general equation but there is some amazing physics hidden in it.

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