4 Answers

K1 = ½mV1²
K2 = ½m(4V1)²
K2/K1 = 16

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16.
Kinetic energy = ½mv². If v gets 4 times bigger, v² get 4² = 16 times bigger.

From the ratio KE/ke = (V/v)^2 = (4v/v)^2 = 16 we see that KE = 16 ke; the energy increases by a factor of 16. ANS.
HINT: When comparing the same variables at different values, using the ratios is the best way to solve the problem. EX: KE/ke = 1/2 mV^2/1/2 mv^2) = (V/v)^2 QED.