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The motion of a particle is described by the equation \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}^{2} \) where \( \boldsymbol{a}= \) \( 15 \mathrm{cm} \) and \( b=3 \mathrm{cm} / \mathrm{sec}^{2} . \) Its instantaneous velocity at time 3 sec will be:

1. \( 36 \mathrm{cm} / \mathrm{sec} \)
2. \( 1 \mathrm{cm} / \mathrm{sec} \)
3. \( 18 \mathrm{cm} / \mathrm{sec} \)
4. \( 32 \mathrm{cm} / \mathrm{sec} \)

Correct answer: \( 36 \mathrm{cm} / \mathrm{sec} \)

Solution

Instantaneous velocity is the time derivative of position. For x = a + bt^2, v = dx/dt = 2bt, so at t = 3 s with b = 3 cm/s², v = 2·3·3 = 36 cm/s.

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