The box slides down the helical ramp such that r = 0.5 m, θ = (0.5t3)rad, and z = (2-0.2t2...

By differentiating, we have

By differentiating, we have

By differentiating, we have

By differentiating, we have

By differentiating, we have

When we have

At:

Component of the box’s velocity is expressed as

The magnitude of the box’s velocity is expressed as

The magnitude of the box’s velocity is

Components of acceleration of the box is expressed as

Accordingly, we have

Accordingly, we have

Magnitude of the acceleration of the box is expressed as

By substituting the values of the parameters into the above relation, we have

Magnitude of the acceleration of the box is