An electron is accelerated from rest to a velocity of 2.0x10^7 m/s.
a) if the electron travelled 0.10m while it was being accelerated, what was its acceleration?
b)How long did the electron take to attain its final velocity?
Please correct me if I'm wrong but I believe the equations I have to use are V2²=V1²+2ad for part a and V=d/t for part b. Thanks for your help.
a. V^2=Vo^2 + 2a*d. Your Eq is correct.
a = (V^2-Vo^2)/2d.
a = (4*10^14-0)/0.2 = 2.0*10^15 m/s^2.
b. V = Vo + at.
t = (V-Vo)/a.
t = (2*10^7-0)/2*10^15 = 1*10^-8 s.
An electron starts from rest travels a distance of 15cm with constant acceleration and hits a television screen at a speed of 3×10^6m/s.Calculate the acceleration of the electon.
is this right?? lol
Well, congratulations on choosing the correct equations. You're on the right track! So let's dive into it:
a) We know the initial velocity, V1 = 0 m/s, the final velocity, V2 = 2.0x10^7 m/s, and the displacement, d = 0.10 m. Plugging those values into the equation V2² = V1² + 2ad, we get:
(2.0x10^7)² = 0² + 2a(0.10)
Now, you just need to solve for acceleration, a. I won't spoil the answer for you. I'm sure you can handle those calculations. Just remember to keep your units consistent.
b) Now, we want to find the time it took for the electron to reach its final velocity. We already know the displacement, d = 0.10 m, and the final velocity, V = 2.0x10^7 m/s. The equation we need to use is V = d/t, which can be rearranged to give us t = d/V.
So, again, plug in the numbers and solve for time, t. Don't forget about units!
I hope this helps, and remember, if you have any more questions, I'm here to provide a little humor along the way.
You are correct in using the equations V2²=V1²+2ad for part a and V=d/t for part b. These equations will help you to find the acceleration in part a and the time taken in part b.
Let's start with part a:
a) To find the acceleration (a), we can use the equation V2² = V1² + 2ad, where V2 is the final velocity, V1 is the initial velocity (0 m/s since it started from rest), d is the distance traveled (0.10 m in this case), and a is the acceleration we want to find.
Substituting the given values into the equation, we have:
(2.0x10^7 m/s)² = (0 m/s)² + 2a * (0.10 m)
Simplifying the equation:
4.0x10^14 m²/s² = 0 + 0.20a
Now, we can solve for 'a':
4.0x10^14 m²/s² = 0.20a
Divide both sides of the equation by 0.20:
a = (4.0x10^14 m²/s²) / 0.20
Calculating the value:
a ≈ 2.0x10^15 m²/s²
Therefore, the acceleration of the electron is approximately 2.0x10^15 m²/s².
Moving on to part b:
b) To find the time taken (t), we can use the equation V = d/t, where V is the final velocity and d is the distance traveled.
Rearranging the equation:
t = d / V
Substituting the given values into the equation, we have:
t = (0.10 m) / (2.0x10^7 m/s)
Calculating the value:
t ≈ 5.0x10^-9 s
Therefore, it took approximately 5.0x10^-9 seconds (or 5 nanoseconds) for the electron to attain its final velocity.
I hope this helps! Let me know if you have any further questions.