Final answer:
The merry-go-round reaches a rotational velocity of 46.9 rev/s after 3.5 seconds and completes approximately 81.725 revolutions in this time.
Step-by-step explanation:
Calculating Rotational Velocity and Revolutions
Given that a merry-go-round starts from rest and accelerates at a constant rate of 13.4 rev/s², we can calculate its rotational velocity after a time period and the number of revolutions it makes in that time. Using rotational kinematic equations, which are analogous to linear kinematic equations, we can solve for part (a) and part (b).
Rotational Velocity After 3.5 Seconds (a)
The angular velocity (ω) after time t can be found using the equation ω = αt, where α is the angular acceleration. For the merry-go-round, α = 13.4 rev/s² and t = 3.5 s, so:
ω = 13.4 rev/s² × 3.5 s = 46.9 rev/s
Number of Revolutions After 3.5 Seconds (b)
To find the number of revolutions, we use the equation θ = 0.5αt², where θ is the angular displacement in revolutions. Plugging in the values:
θ = 0.5 × 13.4 rev/s² × (3.5 s)² = 81.725 revolutions