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Acceleration

The displacem...

Question

The displacement $x$ of a particle along a straight line at time $t$ is given by $x = a_{0} - a_{1} t + a_{2} t^{2}$ . The acceleration of the particle is

a_{0}

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a_{1}

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2 a_{2}

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a_{2}

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Solution

The correct option is C $2 a_{2}$
Acceleration of the particle is given by
$a (t) = \frac{d^{2} x}{d t^{2}} = \frac{d (\frac{d x}{d t})}{d t}$
So, $\frac{d x}{d t} = \frac{d (a_{0} - a_{1} t + a_{2} t^{2})}{d t} = - a_{1} + 2 a_{2} t$
Thus, $a (t) = \frac{d^{2} x}{d t^{2}} = \frac{d (- a_{1} + 2 a_{2} t)}{d t}$
$\Rightarrow a (t) = 2 a_{2}$ , which is constant.

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