Final answer:
The linear velocity of the material point is 1.5 m/s, and the angular velocity change during 5 minutes is 450 radians/min.
Step-by-step explanation:
a. To calculate the linear velocity of the material point, we can use the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius. In this case, the radius is given as 1.5 meters. Since the centripetal acceleration is related to the angular velocity by the equation ac = ω^2r, we can rearrange this equation to solve for ω: ω = √(ac/r). Plugging in the values, we get ω = √(1.5 m/s² / 1.5 m) = √1 = 1 rad/s. Now we can calculate the linear velocity: v = ωr = 1 rad/s * 1.5 m = 1.5 m/s.
b. To find the angular velocity change during 5 minutes, we need to convert the time from minutes to seconds. There are 60 seconds in a minute, so 5 minutes is equal to 5 * 60 = 300 seconds. The angular velocity change is given by the formula Δω = αt, where Δω is the change in angular velocity, α is the angular acceleration, and t is the time interval. Since the centripetal acceleration is the only acceleration acting on the material point, the angular acceleration is equal to the centripetal acceleration. Plugging in the values, we get Δω = (1.5 m/s²) * (300 s) = 450 rad/min.