A car is traveling at 16 m/s .
How fast would the car need to go to double its kinetic energy?
By what factor does the car’s kinetic energy increase if its speed is doubled to 32 m/s ?
i) 16 * √2 ≈ 23 m/s
ii) 2x the speed means 4x the KE.
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When comparing the same factors but at different values, we use ratios. For example KE/ke = 2 = 1/2 mV^2/1/2 mv^2 = (V/v)^2; so V = v sqrt(2) = 16*1.414 = ? m/s ANS You can do the math.
Again KE/ke = (V/v)^2 = 4; so KE = 4 ke, the kinetic energy is quadrupled. ANS.