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An automotive research facility is testing a new design on bumpers to determine the force at which it will break. The formula for Force is F = 1 2 m v 2 Where m is the mass (weight) and v is the velocity (speed)What is the effect on the force if the velocity changes from 5 miles per hour to 10 miles per hour?

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The equation that would allow us to calculate for the force is expressed as,

                                   F = 0.5mv²

If we are to evaluate the use of 5 miles per hour then, the equation would be,

                                   F = 0.5m(5 m/s)² = 12.5m

For the second given speed,
                                 F = 0.5m₁(10 m/s)² = 50m

The fraction between the forces is equal 4. 

Answer: The force increases by 4 units when velocity changes from 5 miles per hour to 10 miles per hour.

Explanation: The force is given by the formula:

[tex]F=\frac{1}{2}mv^2[/tex]

Force when v = 5 miles per hour

[tex]F_1=\frac{1}{2}m(5)^2[/tex]

Force when v = 10 miles per hour

[tex]F_2=\frac{1}{2}m(10)^2[/tex]

Taking ratio of [tex]F_2[/tex] and [tex]F_1[/tex]

[tex]\frac{F_2}{F_1}=\frac{\left(\frac{1}{2}m(10)^2\right)}{\left(\frac{1}{2}m(5)^2\right)}[/tex]

[tex]F_2=4F_1[/tex]

Hence, the force is increased by 4 units when velocity changes from 5 miles per hour to 10 miles per hour.

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