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Answer 1 · 2016-11-07T16:29:14

$E_{a} = 4 E_{b}$ $E_a=4E_b$

$v_{b} : velocity of object before v_{b} = v$ $v_b:"velocity of object before " v_b=v$

$v_{a} : velocity of object after v_{a} = 2 v$ $v_a:"velocity of object after "v_a=2v$

$m : mass of object$ $m:"mass of object"$

$E_{b} : Kinetic energy of object before E_{b} = \frac{1}{2} \cdot m \cdot v_{b}^{2}$ $E_b:"Kinetic energy of object before "E_b=1/2*m*v_b^2$

$E_{a} : Kinetic energy of object after E_{a} = \frac{1}{2} \cdot m \cdot v_{a}^{2}$ $E_a:"Kinetic energy of object after "E_a=1/2*m*v_a^2$

$(E_b)/(E_a)=(cancel(1/2*m)*v_b^2)/(cancel(1/2*m)*v_a^2)$

$"So "v_b=v ; v_a=2v$

$(E_b)/(E_a)=(v^2)/(2v)^2$

$(E_b)/(E_a)=cancel(v^2)/(4cancel(v^2))$

$(E_b)/(E_a)=1/4$

$E_a=4E_b$