Question

A proton is accelerated from rest through a potential difference V0 and gains a speed v0. If it were accelerated instead through a potential difference of 3V0, what speed would it gain? Group of answer choices

Answer 1

`v_(0,new) = v0\sqrt{}2`

Step-by-step explanation:

Initial work done on the proton is given by,
`\DeltaW0 = q V_o`

we know that,
`\DeltaW = \DeltaK.E`

`qV0 = (1/2) m v_0^2`

`v_0 = \sqrt{}2 q V_0 / m` { eq.1 }

If it were accelerated instead through a potential difference of 2V0, then it would gain a speed will be given as :

using the above formula, we have

`v_(0,new) = \sqrt{}2 q (2V0) / m`

`v_(0,new) = \sqrt{}4 q V0 / m`

`v_(0,new) = v0\sqrt{}2`