The motion of a particle is described by the equation $x = a + b t^{2}$ , where $a = 15$ and $b = 3 c m s^{- 2}$ . Its instantaneous velocity at time $3 \sec$ will be.

$36 c m / s e c$

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$18 c m / s e c$

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$16 c m / s e c$

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$32 c m / s e c$

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Solution

The correct option is B
$18 c m / s e c$

Step 1: Given data
The motion of a particle $x = a + b t^{2}$
Value of $a = 15$
Value of $b = 3 c m s^{- 2}$
Time $t$ = $3 \sec$
Step 2: Formula used:
We know that velocity is the rate of change of displacement.
It means $v = \frac{d x}{d t}$
Step 3: Compute the instantaneous velocity:
Using the formula,
the instantaneous velocity can be calculated as
$x = a + b t^{2} \frac{d x}{d t} = 0 + 2 b t v = 2 b t - - - - (1)$
Substitute the known values in the equation $(1)$ to compute velocity,
$v = 2 \times 3 \times 3 v = 18 c m / s e c$
Thus, the instantaneous velocity at time $3 \sec$ will be $18 c m / s e c$ .
Hence, option B is the correct answer.

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