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Derivative from First Principle

A particle st...

Question

A particle starts from origin with uniform acceleration. Its displacement after $t$ seconds is given in meter by the relation $x = 2 + 5 t + 7 t^{2}$ . Calculate the magnitude of Initial velocity

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Solution

Given equation of path of particle is $x = 7 t^{2} + 5 t + 2$

Now,
$v = \frac{d x}{d t} = 14 t + 5$ .

And initial velocity is the velocity of particle at time $t = 0$ . Hence ;
$v_{i} = 14 (0) + 5 = 5 m s^{- 1}$

So the magnitude of Initial velocity is $5 m s^{- 1}$

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