Question

derive Newton's first equation of motion​

Answer 1

☞ Newton's First Equation of Motion :

According to it an object at rest remains at rest, an object in uniform motion remains in uniform motion until or unless an external force is applied on them.

And according to Newton's Second law i.e.

The force applied is directly proportional to the rate of change of linear momentum.

$\boxed{\bold{F\:=\:ma}}$

Here F = Force

m = mass

a = acceleration

If $F_{external}$ = 0

Then ma also equals to zero

ma = 0

But mass can never be zero (0).

So, a = 0

means v (velocity) = constant.

From above we can say that if $F_{external}$ = 0, v = constant (velocity remains constant) until or unless external force is applied, which proves 1st Law of Newton.

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☞ Motion :

An object is said to be in motion when there is no change in position of object with time with respect to it's surrounding.

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Answer 2

Question-

Derive the first equation of motion.

Answer-

Assuming that a body started with initial velocity “u” and after time t it acquires final velocity v due to uniform acceleration a.  

We know acceleration is defined as the rate of change of velocity, also which is given by the slope of the velocity-time graph.

Thus both from definition as well as graph  Acceleration = Change in velocity/Time Taken i.e. a = v-u /t or at = v-u

Therefore, we have: v = u + at