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Where do we find passive and active margins

User AlexWilson
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Final answer:

To find the velocity of the particle when it is at the origin, we set x(t) = 0 and solve for t. Then we can use the position function to find the velocity.

Step-by-step explanation:

To find the velocity of the particle, we need to take the derivative of the position function x(t). Using the chain rule, we have:

v(t) = -sin(t)√t - (1/2)cost√t

At the first instance the particle is at the origin (x=0), we set x(t) = 0 and solve for t:

0 = cost√t

cos(t) = 0

t = (2n + 1)(π/2), where n is an integer

Now we can find the velocity at this time:

v(t) = -sin((2n+1)π/2)√((2n+1)π/2) - (1/2)cos((2n+1)π/2)√((2n+1)π/2)

User Nibnut
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