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Derivation of Position-Velocity Relation by Graphical Method

The initial v...

Question

The initial velocity of a particle is u (at t=0) and the acceleration f is given by $f = a t$ where $a$ is a constant. Which of the following relation is valid?

A

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B

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C

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D

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Solution

The correct option is B

We have $f = \frac{d v}{d t}$

On rearrangement and integration

$\int_{u}^{v} d v = a \int_{0}^{t} t d t$

$v - u = a \frac{t^{2}}{2}$

$v = u + \frac{a t^{2}}{2}$

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