Final answer:
The angle's measure in radians after 0.15 seconds, with an angular velocity of 45 rad/s, would be 6.75 radians. However, this does not match the provided answer choices, indicating a possible error or miscommunication in the question or choices.
Step-by-step explanation:
Given that the point traveled for 0.15 seconds and the angular velocity is constant at 45 rad/s, to find the angle's measure in radians, we multiply the angular velocity by the time elapsed. The calculation is as follows:
Angle in radians (ΔΘ) = Angular velocity (ω) × Time (t)The angle's measure in radians can be calculated using the formulaθ = ωtWhere θ is the angle in radians, ω is the angular velocity in radians per second, and t is the time in seconds. In this case, we are given that the time is 0.15 seconds and we need to find the angle's measure. Since the question specifies that the angle is measured counterclockwise from the 3 o'clock position, we can use a positive value for the angle.θ = ωtθ = (1 rad/s)(0.15 s) = 0.15π radiansTherefore, the angle's measure is 0.15π radians (c)ΔΘ = 45 rad/s × 0.15 sΔΘ = 6.75 radians.This result provides the angular displacement, but it does not directly match with any of the options provided (a) π radians (b) 0.5π radians (c) 0.15π radians (d) 0.3π radians. Therefore, we must clarify the context or values given in the question to select the appropriate answer from the options provided.