What's wrong? Electron acceleration

[studypersist]

I am working on this problem but I got it wrong. I'm not sure what happened.

Homework Statement

An electron with initial velocity Vo = 2.3e5 m/s enters a region 1.0 cm long where it is electrically accelerated. It emerges with velocity v = 4.10e6 m/s. What was its acceleration, assumed constant?

_________ m/s^2

Homework Equations

DeltaX = 1/2 (Vo + V)t

V = Vo +at

The Attempt at a Solution

I thought these were my known variables:

Vo = 2.3e5 m/s
DeltaX = 1.0 cm
Vf = 4.10e6 m/s

I tried to solve for t using DeltX equation. I got 4e-9 s. Then I tried to solve for a using my new value for t and V equation. I got 9.675e14 m/s^2 which is wrong. So anyone know what happened?

 

[HallsofIvy]

Vr+V0= 4100000+ 230000= 433000 or 4.33 e⁵ m/s. Half of that is 2.665 e⁵ and deltax= 1 cm= 0.01 m. t= 0.01/(2.665 e⁵= 3.75 e^-8 s, not -9. Try your calculation again, not using scientific notation this time. That may be what is confusing you.

Vf- V0= 4100000- 230000= 387000 or 3.87 e⁵ m/s. Dividing that by 3.75 e^-8 gives an acceleration of 1 x 10¹⁴ m/s². Your equations are right. Check your arithmetic.

 

[studypersist]

Thank you. When I solved for t, i got .000000004 and I thought it would be like totally okay to just use 4e-9. When I tried it again I got a more specific number by using SN button on my calculator. Using 4.6189e-9 for t, I got the right answer. 8.37855e14