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Question:
why is gravity and acceleration used in the formula s = ut+1/2at^2
Answer:

This equation of motion S= ut+(1/2)at

is the relation of, initial velocity u, time t, distance covered by object S and the uniform motion of object a.

So,in case of vertical motion we consider gravitational acceleration g.

For an object, which is moving downwards (towards earth) we take positive g. And for the upwards motion we take acceleration as -g.

The value of g= 9.8 m/sec2

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