# Homework Help: Connection between potential difference and velocity?

1. Jan 28, 2012

### mirandab17

Hey there!

Having some difficulty with this question... is there any proportionality law between potential difference and velocity?

An electric charge accelerated from rest through a potential difference of 250 V reaches a speed of 9.4 x 10^6 m/s. What speed will this same charge reach if it is accelerated by a potential difference of 125 V?

So I started with conservation of energy. Ek = Ep.

(.5)mv^2 = Ue = qV

But how can I complete this without knowing its mass or quantity of charge?

2. Jan 28, 2012

### Staff: Mentor

Just assume that the mass and charge are constant. If you set up the problem in the form of a ratio these constants will cancel out.

3. Jan 28, 2012

### mirandab17

If I set it up as a ratio:

2V/v^2 = 2V/v^2

So would I set it up as 2(250)/(9.4x10^6)^2 = 2(125)/v^2

4. Jan 28, 2012

### Staff: Mentor

You should differentiate the V's and v's, perhaps by giving them subscripts to denote 'old' value and 'new' value. Note that you can also cancel the 2's which appear on each side of your equation -- just another constant that vanishes when you use ratios!

But yes, your setup will work.