The angular speed of a propeller on a boat increases with constant acceleration from 11 rad/s to 26 rad/s in 2.4 seconds. Through what angle did the propeller turn during this time?

Vo t + (1/2) a t^2

a = change in speed/change in time = (26-11)/2.4 = 6.25 rad/sec^2

so
11* 2.4 + (1/2) *6.25 * 2.4^2

To find the angle turned by the propeller during the given time interval, we can use the following formula:

θ = ω₁t + 0.5αt²

where:
θ is the angle turned
ω₁ is the initial angular speed
t is the time interval
α is the angular acceleration

Given:
ω₁ = 11 rad/s (initial angular speed)
ω₂ = 26 rad/s (final angular speed)
t = 2.4 seconds (time interval)

First, let's calculate the angular acceleration (α):
α = (ω₂ - ω₁) / t

Substituting the given values:
α = (26 rad/s - 11 rad/s) / 2.4 s
α = 15 rad/s / 2.4 s
α ≈ 6.25 rad/s²

Now, let's substitute the known values and solve for θ:
θ = ω₁t + 0.5αt²
θ = 11 rad/s * 2.4 s + 0.5 * 6.25 rad/s² * (2.4 s)²
θ = 26.4 rad + 0.5 * 6.25 rad/s² * 5.76 s²
θ = 26.4 rad + 18 rad
θ ≈ 44.4 rad

Therefore, the propeller turned approximately 44.4 radians during the given time interval.

To find the angle turned by the propeller, we can use the formula:

θ = ω₀t + (1/2)αt²,

where:
θ = angle turned by the propeller,
ω₀ = initial angular speed of the propeller,
t = time, and
α = acceleration.

Given:
ω₀ = 11 rad/s (initial angular speed),
ω = 26 rad/s (final angular speed),
t = 2.4 s (time).

We need to find θ.

We can start by finding the acceleration (α) using the formula:

α = (ω - ω₀) / t.

Substituting the given values:

α = (26 rad/s - 11 rad/s) / 2.4 s = 6.25 rad/s².

Now, we can substitute the values of ω₀, t, and α into the formula for θ:

θ = (11 rad/s)(2.4 s) + (1/2)(6.25 rad/s²)(2.4 s)².

Simplifying the equation:

θ = 26.4 rad + 17.28 rad = 43.68 rad.

Therefore, the propeller turned through an angle of 43.68 radians during this time.