To find the distance traveled (arc length, [tex]\( s \)[/tex]) of a point moving with a constant speed, we start with the given speed [tex]\( v \)[/tex] and time [tex]\( t \)[/tex]:
1. The speed is given as [tex]\( v = 3.6 \)[/tex] miles per hour (mi/hr).
2. The time is given as [tex]\( t = 30 \)[/tex] minutes. We need to convert this into hours since the speed is given in miles per hour. There are 60 minutes in an hour, so:
[tex]\[
t = \frac{30 \text{ minutes}}{60 \text{ minutes per hour}} = 0.5 \text{ hours}
\][/tex]
3. Now, to find the distance traveled, we use the formula for distance:
[tex]\[
s = v \times t
\][/tex]
Substituting the given values:
[tex]\[
s = 3.6 \, \text{mi/hr} \times 0.5 \, \text{hours}
\][/tex]
4. Performing the multiplication:
[tex]\[
s = 1.8 \text{ miles}
\][/tex]
Therefore, the distance traveled [tex]\( s \)[/tex] is:
[tex]\[
s = 1.8 \text{ miles}
\][/tex]
