In the figure, point $\mathrm{P}$ moves at a constant rate along the unit circle. Complete the sentence below.
If $P$ is rotating with angular speed $\frac{\pi}{2}$ radians per sec, then the distance traveled by $P$ in 10 seconds is units.
If $P$ is rotating with angular speed $\frac{\pi}{2}$ radians per sec, then the distance traveled by $P$ in 10 seconds is $\square$ units. (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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.