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Find the velocity of a particle with the given acceleration: a(t) = 3k, v(0) = 16i - 3j. (Select the correct answer)

A. v(t) = (16t - 9)i + 3tk
B. v(t) = ...

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Final answer:

To find the particle's velocity given an acceleration of a(t) = 3k and initial velocity v(0) = 16i - 3j, we integrate the acceleration and apply the initial condition, resulting in v(t) = 3kt + (16i - 3j).

Step-by-step explanation:

To find the velocity of a particle with the given acceleration function a(t) = 3k and the initial velocity v(0) = 16i - 3j, we integrate the acceleration function with respect to time.

Integrating a(t) = 3k with respect to time gives us the velocity function v(t), considering the constant vector c for the integration:

v(t) = ∫ a(t) dt = ∫ 3k dt = 3kt + c

Using the initial condition v(0) = 16i - 3j, we find that:

c = 16i - 3j

Therefore, the velocity function is:

v(t) = 3kt + (16i - 3j)

This provides us with the correct expression for the velocity of the particle as a function of time.

User Daniel Alder
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