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How to Derive Velocity and Displacement Formulas of Uniformly Accelerated Linear Motion with Advanced Mathematics
Velocity v and displacement x of uniformly accelerated linear motion.

The acceleration is a, the velocity is v, and the displacement is X.

At this time, a is a constant,

Velocity v

v =? ∫adt

= at + c 1

Here c 1 = v0.

The above formula is,

v =? ∫adt

= at+v0

————————————————————

Displacement x

x =? ∫vdt

= ∫(at + v0)dt

= at? /2 + v0t + c2

Here, c2 = x0

The above formula is,

x =? ∫vdt

=? ∫ (at+v0) dt

= at? /2 + v0t + x0