If the velocity of a particle is $(10 + 2 r^{2})$ m/s then the average acceleration of the particle between 2s and 5s is

2 m / s^{2}

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4 m / s^{2}

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12 m / s^{2}

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14 m / s^{2}

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Solution

The correct option is D $14 m / s^{2}$
The velocity equation is
$v = (10 + 2 t^{2}) m / s$
$v_{t = 2 s e c} = 10 + 2 \times 2 \times 2 = 18 m / s$
$v_{t = 5 s e c} = 10 + 2 \times 5 \times 5 = 60 m / s$
Average acceleration,
$a_{a v g} = \frac{v_{t = 5 s e c} - v_{t = 2 s e c}}{5 - 2} = \frac{60 - 18}{3}$
$a_{a v g} = 14 m / s^{2}$
The correct option is D.

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