The velocity of a particle is given by v = {16t'i + 4t°j + (5t + 2)k} m/s, where t is in seconds. If the particle if at the origin when t = 0, determine the z-coordinate position %3D of the particle when t = 2 s.

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A: Given, r(t)=lnsecti^+tj^

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A: Solution:-Given thatRadius of circular path (R)=5 ftθ=e0.5t rad where t is in secondswhen θ=90°

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A: See below

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A: Given: a→t=24t2+1i^+tj^+6t2-2tk^, Starting point O(0, 0, 0)

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A: since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A: Required : Velocity of the object when it reaches the maximum y-coordinate.

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Q: Question 4: A particle is thrown into air with initial speed vo making angle 0 with the horizontal…

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: Given: The acceleration is given as, at=5sint-2cost Positions are, s0=0s2π=4

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A: The coordinates are given by: ρ=4ϕ=2tz=0.5t2 The above coordinates can be written as:…

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Q: A particle is sliding in a circular path, using polar coordinates where r = 2 and 0 =21 so that the…

A: Polar coordinate (r) = 2 m θ = 2 t