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Average Velocity in 2D Motion

The position ...

Question

The position of a particle moving along the $x -$ axis is expressed as $x = {a t}^{3} + {b t}^{2} + c t + d$ . The initial acceleration of the particle is

6 a

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2 b

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a + b

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a + c

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Solution

The correct option is B $2 b$
The relationship between position and time is given by the equation,
$x = a t^{3} + b t^{2} + c t + d$
Velocity, $v = \frac{d x}{d t}$
$v = 3 a t^{2} + 2 b t + c$
Acceleration, $a = \frac{d v}{d t}$
$a = 6 a t + 2 b$
The initial acceleration at time $t = 0 s e c$
$a |_{t = 0 s e c} = 6 a (0) + 2 b$
$a |_{t = 0 s e c} = 2 b$
The correct option is B.

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