The particle velocity

Question

What speed must a particle attain before its kinetic energy is double the value predicted by the nonrelativistic expression KE=1/2 mv^2. I know the answer but I don't understand how to obtain it can someone help me?

Answer 1

Kinetic energy = KE = (1/2)mV^2

(KE)1 = (1/2)(m)V1^2

where

m = mass of particle

V1 = velocity of particle

If KE = doubled, then

(KE)2 = (1/2)(m)V2^2

When the kinetic energy is doubled,

(KE)2 = 2 * (KE)1

(1/2)(m)V2^2 = (2)(1/2)(m)V1^2)

Since "m" appears on both sides of the equation, it will simply cancel out, hence the above modifies t

V2^2 = 2V1^2

Solving for V2,

V2 = sqrt 2(V1)

Answer 2

solve KE=1/2 mv^2 with KE=1 to get a velocity.

Then solve for velocity with KE doubled, or 2.

(I dont know what you started with)