How Long Does It Take an Electron to Accelerate to a Specific Speed?

[minhas510]

Homework Statement

an electron has an initial speed of 1.43 * 10^5 m/s^2
if it undergoes an acceleration of 2.3 * 10^14 m/s^2
how long will it take to reach a speech of 7.47 * 10^5 m/s?
Answer in units of s.

and then part B is asking
how far has it traveled in this time? answer in units of m

i need to know how to get the answer, step by step please.

 

[kuruman]

Hi minhas510, welcome to PF. We don't provide answers, just help. You need to show us the relevant equations and your thoughts on the problem. Our rules are quite clear:

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.

So what equations do you think are relevant and how to you think you could possibly use them?

 

[tomcue]

I would approach this problem by first writing out the given information and identifying the unknown variables. We know that the initial speed of the electron is 1.43 * 10^5 m/s and the acceleration is 2.3 * 10^14 m/s^2. The unknown variables are the time it takes to reach a speed of 7.47 * 10^5 m/s and the distance traveled in that time.

To find the time, we can use the equation v = u + at, where v is the final speed, u is the initial speed, a is the acceleration, and t is the time. Rearranging this equation, we get t = (v-u)/a.

Plugging in the values, we get t = (7.47 * 10^5 m/s - 1.43 * 10^5 m/s) / (2.3 * 10^14 m/s^2) = 2.913 * 10^-9 s.

Therefore, it will take the electron approximately 2.913 * 10^-9 seconds to reach a speed of 7.47 * 10^5 m/s.

To find the distance traveled, we can use the equation s = ut + (1/2)at^2, where s is the distance, u is the initial speed, a is the acceleration, and t is the time. Plugging in the values, we get s = (1.43 * 10^5 m/s) * (2.913 * 10^-9 s) + (1/2) * (2.3 * 10^14 m/s^2) * (2.913 * 10^-9 s)^2 = 9.91 * 10^-4 m.

Therefore, the electron will travel approximately 9.91 * 10^-4 meters in the given time.