Why does kinetic energy quadruple if speed doubles?

Why does kinetic energy quadruple if speed doubles?
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1 Answer

Answer :

Work (which is a type of energy transfer) = force xdistance.Look at the formulae for acceleration. The relevantformula in this case (simplified for the case that the initialspeed is zero) is:Distance = (1/2) acceleration time squaredLet's keep the acceleration constant. Note that this will alsomake the force constant. In this case, in twice the time yourobject will move four times the distance. Note that at constantacceleration, in twice the time you get twice the speed (assumingthat you start at speed = 0).Combining all of the above, to get twice the speed, you need toapply the same acceleration (and therefore, the same force) overFOUR times the distance. As a result, the amount of work requiredto achieve this acceleration will also increase by a factor four.Or in general, it will scale with the square of the speed.
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