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A standard Ford F150 has a standard tire size of 25.7 inches in diameter. You decided to replace the standard tires with a tire with a diameter of 28.2 inches without updating the onboard computer. Last week you were stopped for speeding on the highway where the speed limit is 65 mph. With the change in tires, how fast was the truck actually traveling when the speedometer read 65 mph? If you had used 24 inch tires, what would the actual speed have been if the speedometer read 65 mph?

You should develop a document to be presented to the judge that explains your speed if you still had the original 25.7 inch tires, your actual speed with the new 28.2 inch tires, and your speed if you replaced the wheels with 24 inch tires.

Respuesta :

The speed of the truck is higher (or lower) than the speedometer value  

when a larger (or smaller) than standard sized tire.

Responses:

  • The speed with a 28.2 inches tire is actually approximately 71.3 mph
  • The actual speed if a 24 inch tire was used would be 60.7 mph

How does the size of the tire determine the speed?

The standard tire size diameter = 25.7 inches

Diameter of the replacement tire = 28.2 inches

Circumference of the standard tire = π·25.7 inches

1 mile = 63,360 inches

65 miles = 65 × 63,360 inches

[tex]Number \ of \ rotation =\dfrac{63,360 \times 65}{\pi \times 25.7} \approx \mathbf{ 51,008.85}[/tex]

Distance travelled by the replacement tire with the same number of

rotations is therefore;

[tex]Distance =\dfrac{63,360 \ in. \times 65}{\pi \times 25.7 \ in.} \times \pi \times 28.2 \ in. \approx \mathbf{4519022.6\ in.}[/tex]

Actual distance travelled in one hour = 4519022.6 ÷ 63,360 ≈ 71.32

  • The actual speed of the truck when the speedometer read 65 mph is; 71.32 mph

 

Second part; Tire diameter = 24 inches

Distance traveled in one hour = 51,008.85 × π × 24 ≈ 3845976.68

Distance traveled in one hour ≈ 3845976.68 inches

3845976.68 inches ≈ 60.7 miles

The actual speed if a 24 inch tire is used is approximately 60.7 mph

Details of the truck speed with different sized wheels

  • The speed if the original 25.7 inch tires is used will be the speed on the speedometer, which is 65 mph.
  • However the actual speed with the new 28.2 inch tires is approximately 71.32 mph.
  • The speed if the wheels were replaced with a 24 inch tire is approximately 60.7 mph

Learn more about rotation and speed here:

https://brainly.com/question/14745232

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