A car is traveling along a road, and its engine is turning over with an angular velocity of +190 rad/s. The driver steps on the accelerator, and in a time of 13.0 s the angular velocity increases to +300 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity had remained constant at the initial value of +190 rad/s during the entire 13.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +300 rad/s during the entire 13.0-s interval? (c) Determine the actual value of the angular displacement during the 13.0-s interval.

a. D = Vo*t = 190rad/s * 13s = 2470 rad

b. D = 300rad/s * 13s = 3900 Rad.

c. a = (V-Vo)/t = (300-190)/13 = 8.46 rad/s^2.

D = Vo*t + 0.5a*t^2
D = 190*13 + 4.23*13^2 = 3185 Rad.

To solve this problem, we need to use the relationship between angular displacement (θ), angular velocity (ω), and time (t). The formula is:

θ = ω * t

(a) To find the angular displacement if the angular velocity remains constant at +190 rad/s during the entire 13.0-s interval, we can plug the values into the formula:

θ = (190 rad/s) * (13.0 s)
θ = 2470 rad

Therefore, the angular displacement would be 2470 radians.

(b) To find the angular displacement if the angular velocity had been equal to its final value of +300 rad/s during the entire 13.0-s interval, we again use the formula:

θ = (300 rad/s) * (13.0 s)
θ = 3900 rad

Therefore, the angular displacement would be 3900 radians.

(c) To determine the actual value of the angular displacement during the 13.0-s interval, we need to consider the change in angular velocity. The change in angular velocity is given by:

Δω = final angular velocity – initial angular velocity
Δω = 300 rad/s – 190 rad/s
Δω = 110 rad/s

Now, we can use this change in angular velocity to find the actual angular displacement. We will use the formula:

θ = ω * t + 0.5 * Δω * t

θ = (190 rad/s) * (13.0 s) + 0.5 * (110 rad/s) * (13.0 s)
θ = 2470 rad + 0.5 * 1430 rad
θ = 2470 rad + 715 rad
θ = 3185 rad

Therefore, the actual angular displacement during the 13.0-s interval is 3185 radians.