The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h − bt, where c, h, and b are constants. Determine the magnitudes of its velocity and acceleration.

Step-by-step explanation:

Let denotes position of the roller coaster.

Let

Differentiate with respect to t

Here, denotes velocity.

Differentiate again with respect to t

Here, denotes acceleration.

Magnitude of velocity:

Magnitude of acceleration:

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explanation:

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