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Question
Derive the formula : v = u + at, where the symbols have usual meanings.
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Solution
Consider a body has initial velocity (u) . Suppose it is subjected to a uniform acceleration (a) such that after time (t) its final velocity becomes (v). Now, from the definition of acceleration we know that:
Acceleration = `"Change in velocity"/"Time taken"`
The above expression can also be written as ,
`a = (v-u)/t`
On further simplification, we get the 1st equation of motion,
v = u + at
Where,
(a) - Acceleration
(v) - Final velocity
(u) - Initial velocity
(t) - Time taken
The equation v = u + at is called the first equation of motion and is used to calculate the velocity 'v' acquired by a body in time 't'.
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