A merry-go-round initially at rest at an amusement park begins to rotate at time t=0. The angle through which it rotates is described by θ(t)=πk(t+ke−t/k), where k is a positive constant, t is in seconds, and θ is in radians. The angular velocity of the merry-go-round at t=T is

Angular velocity of merry-go-round is πk - 1 at t= T

Explanation:

From the question it is given that

..........................(1)

since mathematically, angular velocity is defined as

........................(2)

on substituing the value of θ(t) from equation 1 in equation (2) we get

=   ............................(3)

on differentiating equation (3) with respect to time we get

ω(t) = πk(1 -) = πk - 1 angular velocity of merry-go-round

Therefore, angular velocity of merry-go-round is πk - 1 at t= T

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

f=ma newton's second law 7x8=56n