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Derivation of three equations of motion

Which of the ...

Question

Which of the following graphs gives the equation $x = v_{0} t + \frac{1}{2} a t^{2}$

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None of these

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Solution

The correct option is C
Given the equation
$x = v_{0} t + \frac{1}{2} a t^{2}$
$\Rightarrow \frac{d x}{d t} = \frac{d (v_{0} t + \frac{1}{2} a t^{2})}{d t}$
$\Rightarrow v = v_{0} + a t$
So, the $v - t$ curve can be shown as

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