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A car traveling at 60 mph has how much more energy than a car going at 20 mph? How many times does the kinetic energy of a car increase when traveling 60 mph as opposed to traveling 30 mph? K.E. increases _____ times.

Respuesta :

Explanation :

(a) Initial velocity, v₁ = 60 mph

Final velocity, v₂ = 20 mph

Let KE₁ and KE₂ are the initial and final kinetic energies.

[tex]\dfrac{KE_1}{KE_2}=\dfrac{1/2mv_1^2}{1/2mv_2^2}[/tex]

[tex]\dfrac{KE_1}{KE_2}=\dfrac{(60)^2}{(20)^2}[/tex]

[tex]\dfrac{KE_1}{KE_2}=9[/tex]

So, the kinetic energy increases 9 times.

(b) Initial velocity, v₁ = 60 mph

Final velocity, v₂ = 30 mph

Let KE₁ and KE₂ are the initial and final kinetic energies.

[tex]\dfrac{KE_1}{KE_2}=\dfrac{1/2mv_1^2}{1/2mv_2^2}[/tex]

[tex]\dfrac{KE_1}{KE_2}=\dfrac{(60)^2}{(30)^2}[/tex]

[tex]\dfrac{KE_1}{KE_2}=4[/tex]

So, the kinetic energy increases 4 times.

Hence, this is the required solution.

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