Particle Displacement - Integration

1. Jun 4, 2009

Noir

1. The problem statement, all variables and given/known data
the velocity v m/s of a body moving in a straight line is given by v = 3t^2 - 4t - 4. if the body has an initial displacement of 3 m from O, find:
*a. the displacement and acceleration at any time t s;
*b. the time when the body is momentarily at rest;
*c. the distance travelled in the first three seconds.
2. Relevant equations
Common Integration

3. The attempt at a solution
Ok so I can do a) and b ) without any troubles. It's c I'm having a problem with. I can do it with a Velocity vs Time graph (Find the area underneath) and just use a number line. Except I can't find a relationship between time and distance. Can anyone help?

2. Jun 4, 2009

Cyosis

How did you find the displacement as a function of time?

3. Jun 4, 2009

Noir

I integrated the velocity function and found a displacement equation;
d(t) = t^3 - 2t^2 -4t + 3.
Except this gives displacement, not distance. Thats why I'm stuck :(

4. Jun 4, 2009

enricfemi

I cant remember the first three seconds mean in high school. But just integration time from o to 3(0r maybe 2).

5. Jun 4, 2009

Cyosis

What's the difference between the displacement and the distance?

6. Jun 4, 2009

Noir

It gives -3 when the answer is 13m.

7. Jun 4, 2009

Noir

"Distance is the scalar value of how far an object has traveled regardless of direction.
Displacement is the vector value of how far an object has been displaced, meaning how far is it from where it started. "

8. Jun 4, 2009

enricfemi

you can know the displacement d(0) while t=0 from the expression. and in the same way, the displacement while t=3. of course you can calculate the distance.

9. Jun 4, 2009

Noir

Distance and Displacement are different. If I sub in 3 for t in the displacement equation I get 0. Can you explain what you said with an equation?

10. Jun 4, 2009

enricfemi

that's it. just minus them

11. Jun 4, 2009

enricfemi

ok, i have figured out your problem.
if u sub in 3 into the equation, it turns out to be 0. what does it mean?
it means the O of axis.

12. Jun 4, 2009

Noir

It means that at 3 seconds the displacement of the body is 0 m from the starting point. This doesn't help me find distance.

13. Jun 4, 2009

enricfemi

the particle first located the position which has displacement of 3m from O. and then moved back to O. how long did it traveled?

14. Jun 4, 2009

enricfemi

O, if you mean the distance not the displacement of the two events, then forget it!
i always misunderstand the high school title.

15. Jun 4, 2009

enricfemi

by using mathematica, i drew a picture of the displacement.

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16. Jun 4, 2009

enricfemi

you can know the rest point from question b), then multiple it by 2, and add the displacement of 3m. finally, you can get the answer.