Question

suppose that point p is on a circle with radius r, and ray op is rotating with angular speed ω. complete parts (a) through (c). r = 6 cm, ω = \frac{\pi}{4} radian per sec, t = 4 sec (a) what is the angle generated by p in time t? θ = π radian (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) (b) what is the distance traveled by p along the circle in time t? s = 6π cm (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) (c) what is the linear speed of p? v = cm per sec (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall linear - speed formula

The formula for linear speed $v$ is $v=\frac{s}{t}$, where $s$ is the arc - length and $t$ is the time.

Step2: Identify known values

We know from part (b) that $s = 6\pi$ cm and $t = 4$ sec.

Step3: Calculate linear speed

Substitute $s = 6\pi$ and $t = 4$ into the formula $v=\frac{s}{t}$, we get $v=\frac{6\pi}{4}=\frac{3\pi}{2}$ cm per sec.

Answer:

$\frac{3\pi}{2}$