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Find the linear speed [tex]\( v \)[/tex] of a point moving with constant speed in a circular motion. The point travels an arc length [tex]\( s = \frac{1}{15} \)[/tex] inches in time [tex]\( t = 8 \)[/tex] minutes.

Enter the exact answer with correct units:

[tex]\[ v = \][/tex]



Answer :

GinnyAnswer
To determine the linear speed [tex]\( v \)[/tex] of a point traveling in a circular motion, we can use the relationship between the arc length [tex]\( s \)[/tex], the time [tex]\( t \)[/tex], and the linear speed [tex]\( v \)[/tex]. The linear speed is given by the formula:

[tex]\[ v = \frac{s}{t} \][/tex]

where:
- [tex]\( s \)[/tex] is the arc length
- [tex]\( t \)[/tex] is the time taken to travel the arc length

Given:
- Arc length [tex]\( s = \frac{1}{15} \)[/tex] inches
- Time [tex]\( t = 8 \)[/tex] minutes

Substitute the given values into the formula:

[tex]\[ v = \frac{1/15 \text{ inches}}{8 \text{ minutes}} \][/tex]

Perform the division:

[tex]\[ v = \frac{1}{15} \div 8 = \frac{1}{15} \times \frac{1}{8} \][/tex]

[tex]\[ v = \frac{1}{15 \times 8} = \frac{1}{120} \][/tex]

So, the linear speed [tex]\( v \)[/tex] is:

[tex]\[ v = \frac{1}{120} \text{ inches per minute} \][/tex]

Converting the fraction to decimal form, we get:

[tex]\[ v = 0.008333333333333333 \text{ inches per minute} \][/tex]

Therefore, the exact linear speed is:

[tex]\[ v = \frac{1}{120} \text{ inches per minute} \][/tex]

And in decimal form, the linear speed is approximately:

[tex]\[ v = 0.008333333333333333 \text{ inches per minute} \][/tex]

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