Find the linear speed of a point that moves with a constant speed in a circular motion if the point travels along a circle of arc length 7.524 miles in 12 minutes. Round your answer to the nearest tenth.

Imagine that we had a rubber tire and we cut out a section of it. This piece is an arc of the full circle (the original uncut tire). Laying the curved cut rubber piece out flat produces a straight line. If a point moves along this line, then it also moves along the piece of the circle.

To find the linear speed, we just need to divide the arc length over the time value.

In our case, we will compute the following:

linear speed = (arc length)/(time elapsed)

linear speed = (7.524 miles)/(12 minutes)

linear speed = (7.524/12) miles per minute

linear speed = 0.627 miles per minute

linear speed = 0.6 miles per minute

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If needed, multiply that by 60 to convert to miles per hour

So we'd say:

(0.6 miles/min)*(60 min/1 hr) = 36 miles per hour

I wasn't sure which units your teacher wanted, so I figured why not show both.