Use the conversion factors to convert inches to miles and also seconds to hours.
A
a
v=2 π r/T
B
b
About 12.5 miles per hour
Practice makes perfect
a
We are given that the speed v of an object spinning in a circle equals the circumference of the circle divided by the time T it takes the object to complete one revolution. Let's write the defined speed of a spinning object.
Speed = Circumference/TimeWe want to write above formula using the variables v, T, and r (the radius of the circle). To do so, let's first remember the formula for the circumference of the circle.
Circumference = 2 π r
Now we can substitute Speed= v, Circumference= 2 π r, and Time= T into the speed formula.
v = 2 π r/T
b
We are given that a scooter has tires with a radius of 3 12 inches and the tires make one revolution every 110 seconds. To find the scooter's speed, we will substitute r= 3 12 and T= 110 into the formula that we found in Part A.
We found that the speed of the scooter is about 219.9 inches per second. However, we are asked to find the speed in miles per hour. To do so we will first convert our speed in inches to miles using a conversion factor.
1mile/63 360inches
Multiplying 219.9 inches by this factor will convert it to miles.
Next, we will convert this value in miles per second to miles per hour. To do so we will use the second conversion factor.
3600seconds/1hour
To get an accurate value, we will multiply ( 219.963 360) miles per second by the second conversion factor. Let's do it!
