The motion of a body is described by the equation $\frac{d v (t)}{d t} = 6 - 3 v (t)$ where $v (t)$ is the speed (in $m s^{- 1}$ ) at time t (in s). If the body was at rest at t = 0, the magnitude of the initial acceleration is

$3 m s^{- 2}$

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$6 m s^{- 2}$

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$9 m s^{- 2}$

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zero

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Solution

The correct option is B
$6 m s^{- 2}$

Given that, $\frac{d v (t)}{d t} = 6 - 3 v (t)$
Since at t = 0, v = 0, the acceleration at t = 0 is
$a (0) = {\frac{d v (t)}{d t} ∣ ∣}_{t = 0} = 6 - 0 = 6 m s^{- 2}$
Thus, the correct choice is (b).

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The motion of a body is described by the equation $\frac{d v (t)}{d t} = 6 - 3 v (t)$ where $v (t)$ is the speed (in $m s^{- 1}$ ) at time t (in s). If the body was at rest at t = 0, the magnitude of the initial acceleration is

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The motion of a body is described by the equation dv(t)dt=6−3v(t) where v(t) is the speed (in ms−1) at time t (in s). If the body was at rest at t = 0, the magnitude of the initial acceleration is

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The motion of a body is described by the equation $\frac{d v (t)}{d t} = 6 - 3 v (t)$ where $v (t)$ is the speed (in $m s^{- 1}$ ) at time t (in s). If the body was at rest at t = 0, the magnitude of the initial acceleration is

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Given that, $\frac{d v (t)}{d t} = 6 - 3 v (t)$
Since at t = 0, v = 0, the acceleration at t = 0 is
$a (0) = {\frac{d v (t)}{d t} ∣ ∣}_{t = 0} = 6 - 0 = 6 m s^{- 2}$
Thus, the correct choice is (b).