$\"\"$

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(a)

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Find the angular speeds of the tires.

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Vehicle’s tires range between $\"\"$ and $\"\"$ revolutions per minute.

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The diameter of each tire is $\"\"$ inches.

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$\"\"$

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Case 1 :

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If number of rotation in revolutions of the tires per minute is $\"\"$ .

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Angle of each rotation of tire is $\"\"$ .

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Angle of $\"\"$ rotations is $\"\"$ .

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Angular speed of the tire is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Case 2 :

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If number of rotation in revolutions of the tires per minute is $\"\"$ .

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Angle of each rotation of tire is $\"\"$ .

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Angle of $\"\"$ rotations is $\"\"$ .

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Angular speed of the tire is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Angular speeds of the tires is $\"\"$ to $\"\"$ .

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$\"\"$

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Find the linear speeds of the tires.

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If number of rotation in revolutions of the tires per minute is $\"\"$ .

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Tire diameter $\"\"$ .

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$\"\"$

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Radius $\"\"$ .

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The linear speed is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute equation (2) and (3) in equation (1).

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$\"\"$

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Case 2 :

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If number of rotation in revolutions of the tires per minute is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Linear speeds of the tires is $\"\"$ to $\"\"$ .

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$\"\"$

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(a) Angular speeds of the tires is $\"\"$ to $\"\"$ .

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(b) Linear speeds of the tires is $\"\"$ to $\"\"$ .