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A particle is moving along a curved path described by the equation r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j. Determine the velocity of the particle at a given value of θ.

User Reed Morse
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2 Answers

4 votes

Answer:

Explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

User Mervin
by
7.9k points
2 votes

Explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

User Lawrence Barsanti
by
8.0k points

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