How Long Does an Electron Accelerate in a Particle Accelerator?

[RyanH42]

Homework Statement

Could you help me with this one?

"In a particle accelerator, an electron enters a region in which it accelerates uniformly in a straight line from a speed of $4.00x10^5$ m/s to a speed of $6.00x10^7$ m/s in a distance of 3.00 cm. For what time interval does the electron accelerate?''

Homework Equations

$x-x_0=1/2(v+v_0)t$

The Attempt at a Solution

$x-x_0=0.03m$, $(v+v_0)=604.10^5$ so $0.06m=604.10^5t$
t=0.06/604.10^5)
t=0.0000993377.10^-5s = 9.9.10^-10 s
the answer is 9.38ns whiich its 9.38.10^-9 s
Where I am making wrong

 

[vela]

Your calculation looks fine to me. Perhaps there's a typo in the problem.

 

[RyanH42]

maybe ??

 

[haruspex]

The given answer corresponds to an acceleration up to 6x10⁶ m/s.