Final answer:
The linear velocity of the robot is approximately 2.8125π feet/second.
Step-by-step explanation:
To calculate the linear velocity of the robot, we need to find the distance traveled by the wheel per unit of time. The formula for linear velocity is given by v = ωr, where ω is the angular velocity and r is the radius of the wheel.
First, we need to convert the motor shaft speed from rpm to radians per second. Since 1 revolution is equal to 2π radians, we can find the angular velocity by multiplying the motor speed by 2π. In this case, the angular velocity (ω) is equal to (150 rpm) * (2π radians/1 minute) * (1 minute/60 seconds) = 15π radians/second.
Next, we can calculate the linear velocity by multiplying the angular velocity by the radius of the wheel. The wheel has a diameter of 6 inches, which is equivalent to a radius of 6/2 = 3 inches = 0.25 feet. Therefore, the linear velocity is (15π radians/second) * (0.25 feet) = 3.75π feet/second.
To find the loaded velocity of the robot, we need to consider the efficiency of the system. Since the efficiency is given as 75% or 0.75, the actual loaded velocity is equal to 0.75 times the calculated linear velocity. Therefore, the loaded velocity is 0.75 * 3.75π = 2.8125π feet/second.