Question

A block moves outward along the slot in the platform with a speed of r˙=(2t)m/s, where t is in seconds. The platform rotates at a constant rate of θ˙ = 4 rad/s .

Part A
If the block starts from rest at the center, determine the magnitude of its velocity when t=1s.
Part B
If the block starts from rest at the center, determine the magnitude

Answer 1

The magnitude of the block's velocity when t = 1s is 8 m/s.

Step-by-step explanation:

In this problem, we are given the speed of the block and the angular velocity of the platform. To find the magnitude of the block's velocity at t = 1s, we can use the formula for the velocity of an object moving in a circle:

v = r * ω

where v is the velocity, r is the radius of the circle, and ω is the angular velocity. In this case, the block is moving in a circular path with radius r = 2t and the platform has an angular velocity of ω = 4. Plugging in the values, we get:

v = (2t)(4)

Simplifying the expression, we get:

v = 8t

Substituting t = 1s, we can find the magnitude of the block's velocity:

v = 8(1) = 8 m/s

Therefore, the magnitude of the block's velocity when t = 1s is 8 m/s.