Connection between potential difference and velocity?

[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?

Thanks in advance!

 

[gneill]

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?

Thanks in advance!

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.

 

[mirandab17]

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.

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

 

[gneill]

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

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.