Step 1 :The distance traveled by a point moving along a circle is given by the formula \(d = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the angle in radians.
Step 2 :In this case, the radius of the circle is 1 unit (since it's a unit circle), and the angle is the angular speed times the time.
Step 3 :The angular speed is \(\frac{\pi}{2}\) radians per second, and the time is 10 seconds.
Step 4 :So, the angle is \(\frac{\pi}{2} \times 10 = 5\pi\) radians.
Step 5 :Therefore, the distance traveled by the point is \(1 \times 5\pi = 5\pi\) units.
Step 6 :Final Answer: The distance traveled by \(P\) in 10 seconds is \(\boxed{5\pi}\) units.