## anonymous 4 years ago An electron, starting from rest and moving with a constant acceleration, travels 2.0 cm in 5.0 ms. What is the magnitude of this acceleration?

1. JamesJ

What's the equation of motion for a body under constant acceleration?

2. JamesJ

Suppose v = initial velocity t = time a = constant acceleration Then what is the formula for the distance, d, the object moves in time t? d = ... what?

3. Kainui

What is the definition of acceleration? It's the change of velocity with respect to time. How would you put this in the form of an equation?

4. JamesJ

I'm going to change notation slightly, writing now u for initial velocity. Then we have: u = initial velocity t = time a = constant acceleration Write also v(t) = velocity of object at time t d(t) = position of object at time t Now, by definition, acceleration = (change in velocity)/(Time) hence $a = \frac{v(t) - u}{t}$ thus $v(t) - u = at$ and $v(t) = u + at$ Making sense so far?

5. anonymous

Yeah, I'm following

6. JamesJ

Now, what's d(t) ?

7. anonymous

The position?

8. JamesJ

yes, what's the formula for it?

9. anonymous

v1t + 1/2 a t^2?

10. JamesJ

Yes $d(t) = ut + \frac{1}{2}at^2$ For your problem, you're told that the initial velocity is zero, t = 0.5 ms and d(0.5 ms) = 0.92 m Now calculate a.

11. JamesJ

*correction, d(0.5 ms) = 0.02 m, not 0.92.

12. anonymous

would I try and get a by its self?

13. JamesJ

Thus u = 0 m/s t = 0.005 s d = 0.02 m Substitute that into the equation above and solve for a

14. anonymous

.02 = 0(.005) + .5(a)(.005)^2?

15. JamesJ

yes

16. anonymous

So if a=(v(t)−u)/t, that would equal v(t)/t, correct?

17. JamesJ

yes

18. JamesJ

but here velocity is not constant so you have to be very careful with that formula

19. anonymous

But the velocity equation is dependent on the acceleration equation: v(t)=u+at

20. JamesJ

Yes, so here because acceleration is constant, we're good. I.e., the average acceleration is equal to the constant acceleration.

21. anonymous

But the closest we got to solving for a is: .02 = 0(.005) + .5(a)(.005)^2 and v(t) needs a, v(t)=u+at I'm not getting this part, how do we solve for either one?

22. anonymous

?

23. JamesJ

The question only asks you to find the acceleration. Hence you only need one equation and the one that is germane here--because it uses the information of the problem--is the the one into which you've already substituted.

24. JamesJ

Hence you have: .02 = 0(.005) + .5(a)(.005)^2 This already simplifies to $\frac{0.005^2}{2}a = 0.02$ Now solve for $$a$$.

25. anonymous

A = .02(2/.005^2) = .04/.005^2?

26. JamesJ

Evaluate it. You can't leave the answer in that form.

27. anonymous

1600?

28. anonymous

What about the units though, is that in meters?

29. JamesJ

We were (or at least I was) careful to convert all the units into SI units before we started calculating time = seconds distance = meters velocity = meters/sec = m/s acceleration = m/s^2

30. anonymous

Ah, so its 1.6 km/s^2?

31. JamesJ

yes

32. anonymous

Awesome! Thanks for all your help!