# Proton being accelerated

1. The problem statement, all variables and given/known data

A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

3. The attempt at a solution

Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at... but I can't see how that helps.

Help me begin?

Last edited:

#### LowlyPion

Homework Helper
1. The problem statement, all variables and given/known data

A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

3. The attempt at a solution

Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at^2... but I can't see how that helps.

Help me begin?
You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2

#### ffrog

no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser

#### LowlyPion

Homework Helper
no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser
And what is the time the proton is in the machine?

You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2

So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.

#### LowlyPion

Homework Helper
So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.
Yes the V2 = Vi2 + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.

Yes the V2 = Vi2 + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.
Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?

#### LowlyPion

Homework Helper
Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?
Half right anyway.

... i.e don't forget the 1/2.

Half right anyway.

... i.e don't forget the 1/2.
haha yes! I knew that I was just typing in a hurry.

Thanks.

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