Homework Help: Electron acceleration plot

1. Oct 4, 2009

emyt

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

an electron starting from rest has an acceleration that increases linearly with time, a= kt.
k = 1.5ms^2/s

Plot acceleration v.s. time graph for 10 seconds

Estimate electron's velocity 5.0s after its motion starts

2. Relevant equations
vx =vx0 + axt

3. The attempt at a solution

a = 1.5(5) = 7.5

v = 7.5(5) = 37.5

the velocity at 5 seconds is 37.5 m/s?

thanks

2. Oct 4, 2009

Vykan12

You used a kinematics formula that only applies if acceleration is constant. You have to integrate the given expression for acceleration to get the correct one for velocity.

You should get something like $$v(t) = v_{0} + \frac{1}{2}kt^2$$

3. Oct 4, 2009

emyt

thanks, that's strange that equation isn't in my book - how do you come up with it?

thanks again

4. Oct 4, 2009

Vykan12

There's no equation for it because there's infinitely many ways that acceleration can vary as a function of time.

Eg/

$$a(t) = \sin(t)$$

$$v(t) = \int_{0}^{t} \sin(t) \, dt = -\cos(t) + C$$

5. Oct 4, 2009

emyt

is there a way to "estimate" the velocity after 5 seconds without integration? I'm pretty sure we aren't expected to use this method 2 chapters into the book

thanks

6. Oct 4, 2009

Vykan12

You could draw a graph and find the area of the triangle formed by the line, the y axis and some line x=a.

7. Oct 4, 2009

emyt

okay, to plot a velocity graph, do I just take the acceleration values at each point and use those as slopes?

so if the acceleration at 5 seconds is 7.5 m/s^2 then ill have a 7.5x + c tangent line?

thanks

Last edited: Oct 4, 2009
8. Oct 4, 2009

emyt

Im not sure what you mean.. if you wanted to find the acceleration at a specific point, how do you draw a triangle?

thanks

9. Oct 4, 2009

emyt

hello, I'm waiting :( I sincerely need help, thanks

10. Oct 4, 2009

Vykan12

Do you understand why the area of a rectangle in a graph of acceleration versus time is an estimation of instantaneous velocity?

Recall that for constant acceleration we have a = v/t so v= at.

I really can't explain this properly without the use of calculus. Maybe someone else can.

11. Oct 4, 2009

emyt

yes, because it's acceleration times time

okay, so do I take the area of a super small interval of the graph?

thanks

12. Oct 4, 2009

Vykan12

See the attachment I just posted.

Edit: Sorry, t should be 5 in that graph and a should be (1.5)(5) = 7.5.

Attached Files:

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13. Oct 4, 2009

emyt

thanks so much, I'll look at it when it's finished pending approval

14. Oct 4, 2009

emyt

how long does it take for a picture to pend approval? :|

15. Oct 4, 2009

Vykan12

Forget the attachment. I'll use image shack from now on.

http://img34.imageshack.us/img34/4853/areatriangle.jpg [Broken]

Last edited by a moderator: May 4, 2017
16. Oct 4, 2009

emyt

hi, I see that you got 7.5, how did you get 7.5 = 18.75?

thanks

17. Oct 4, 2009

Vykan12

It should say (0.5)(5)(7.5) = 18.75. The equation got cut into 2 lines by accident.

18. Oct 4, 2009

emyt

:S weird.. I actually tried that before but I couldn't get the right answer, I guess I miscalculated something and threw out the whole plan... the constant acceleration formula works because its at the instant of 5 seconds right?

and I can plot the velocity versus time graph by just doing various points..et c?

thanks a lot

19. Oct 4, 2009

Vykan12

You're wrong on both counts. The constant acceleration formula cannot be used unless the graph of a versus t is a horizontal line. As for the v versus t graph, you need to compute the area from 0 to t_{1}, then from 0 to t_{2}, then from 0 to t_{3} and so on to plot various points v(1), v(2), v(3), etc.

Again, just wait for these kinematics topics to be covered in more detail in class or your book or wherever you're learning from.

20. Oct 4, 2009

emyt

"the constant acceleration formula cannot be used unless the graph of a versus t is a horizontal line. "

oh right, you just did the area under the curve, I mistook that as the v = at formula

" As for the v versus t graph, you need to compute the area from 0 to t_{1}, then from 0 to t_{2}, then from 0 to t_{3} and so on to plot various points v(1), v(2), v(3), etc."

yeah that's what I meant by doing various points.. at least partially, since I was thinking about the wrong formula anyway

thanks a bunch! :)