To find the linear velocity [tex]\( v \)[/tex] of a point moving with uniform circular motion given the distance [tex]\( s \)[/tex] and the time [tex]\( t \)[/tex], we can use the basic formula for linear velocity. The formula is:
[tex]\[ v = \frac{s}{t} \][/tex]
where [tex]\( v \)[/tex] is the linear velocity, [tex]\( s \)[/tex] is the distance covered, and [tex]\( t \)[/tex] is the time taken to cover that distance.
Given:
- Distance covered, [tex]\( s = 8 \)[/tex] feet
- Time taken, [tex]\( t = 4 \)[/tex] minutes
We substitute these values into the formula:
[tex]\[ v = \frac{8 \text{ ft}}{4 \text{ min}} \][/tex]
Now, we perform the division:
[tex]\[ v = \frac{8}{4} \text{ ft/min} \][/tex]
[tex]\[ v = 2 \text{ ft/min} \][/tex]
Therefore, the linear velocity [tex]\( v \)[/tex] is [tex]\( 2 \text{ ft/min} \)[/tex].
