Final answer:
The linear speed of an object moving in a circular path with a diameter of 8 meters, making a 192° turn in 15 seconds, is approximately 0.89 meters per second, which rounds to 0.88 m/s.
Step-by-step explanation:
The student is asking about calculating the linear speed of an object moving in a circular path. Given that the object creates a central angle of 192° in 15 seconds, and the circle's diameter is 8 meters, we can find the object's linear speed. We'll first convert the angle in degrees to radians (192° = 192° x (π/180°) = 3.35 rad) and then use the formula to calculate the circumference (C = πd, where d is the diameter) to find the arc length corresponding to the angle.
Firstly, the circumference of the circle is C = π×8 meters = 25.13 meters. Since the object covers 192°10% of the full circle's circumference, the arc length covered is 3.35 rad/2π rad × 25.13 meters = 13.41 meters in 15 seconds. Finally, we calculate the linear speed which is the arc length divided by time: 13.41 meters / 15 seconds = 0.894 meters/second.
Therefore, the linear speed of the object is approximately 0.89 m/s (which can be rounded to 0.88 m/s if we're considering significant digits).