A Ferris wheel, rotating initially at an angular speed of 0.50 rad/s, accelerates over a 4.0-s interval at a rate of 0.10 rad/s2. What angular displacement does the Ferris wheel undergo in this 7.00-s interval?Select one:a.0.80 radb.2.80 radc.2.20 radd.3.60 rade.​2.40 rad

To solve this problem, we need to use the equations of motion.

First, we need to find the final angular speed after the acceleration. We can use the equation:

final speed = initial speed + acceleration * time final speed = 0.50 rad/s + 0.10 rad/s² * 4.0 s = 0.90 rad/s

Next, we need to find the total angular displacement. This is the sum of the displacement during the initial constant speed and the displacement during the acceleration.

The displacement during the initial constant speed is given by:

displacement = speed * time displacement = 0.50 rad/s * 4.0 s = 2.0 rad

The displacement during the acceleration is given by:

displacement = initial speed * time + 0.5 * acceleration * time² displacement = 0.50 rad/s * 3.0 s + 0.5 * 0.10 rad/s² * (3.0 s)² = 1.5 rad + 0.45 rad = 1.95 rad

So the total angular displacement is 2.0 rad + 1.95 rad = 3.95 rad

However, this is not one of the options. There may be a mistake in the problem or the options.

To solve this problem, we need to use the equations of motion.

First, we calculate the final angular speed using the equation:

ωf = ωi + αt

where: ωf = final angular speed ωi = initial angular speed = 0.50 rad/s α = angular acceleration = 0.10 rad/s² t = time = 4.0 s

Substituting the values, we get:

ωf = 0.50 rad/s + 0.10 rad/s² * 4.0 s = 0.90 rad/s

Next, we calculate the angular displacement for the first 4 seconds using the equation:

θ1 = ωit + 0.5α*t²

Substituting the values, we get:

θ1 = 0.50 rad/s * 4.0 s + 0.5 * 0.10 rad/s² * (4.0 s)² = 2.40 rad

For the remaining 3 seconds, the Ferris wheel is moving at a constant speed (0.90 rad/s), so the angular displacement is simply:

θ2 = ωf * t = 0.90 rad/s * 3.0 s = 2.70 rad

Adding the two displacements together gives the total angular displacement:

θ = θ1 + θ2 = 2.40 rad + 2.70 rad = 5.10 rad

So, none of the options given in the question are correct. The correct answer should be 5.10 rad.