# Particle Dynamics Problem

1. Jan 30, 2007

### s4orce

A particle is moving along a straight line such that its acceleration is defined as a=(4s^2)m/s^2, where s is in meters. If v=-100m/s when s=10m and t=0, determine the particles velocity as a function of position.

Now I'm taking the integral of a but when I plug in the other parts, it doesn't work out. I think I'm doing something wrong.

Someone please comment on how-to approach this problem step by step thanks!

2. Jan 30, 2007

### Cyrus

$$a(t)= \frac{d(s')}{dt} =4s^2$$

Move over dt integrate, set the limits, and solve.

3. Jan 30, 2007

### s4orce

Can you explain a little further please?

4. Jan 30, 2007

### Cyrus

Which part?

What dynamics book are you using? There should be a problem similar to this given somewhere as an example.

5. Jan 30, 2007

### s4orce

after moving over dt to integrate, how did you approach it from there

6. Jan 30, 2007

### Cyrus

what do you mean? Show me some work please.

7. Jan 30, 2007

### s4orce

how can i post the work here?

8. Jan 30, 2007

### Cyrus

Type out what you got and what you did.

You can use [tex] and [ / tex] tags to make it look nicer.

9. Jan 30, 2007

### s4orce

integral 4s^2 = (4s^3)/3

s=10

4(10^3)/3 = 1333.33

1333.33/10 = 133.33 = particle velocity at x position

10. Jan 30, 2007

### Cyrus

Are you familiar with the definition of acceleration?

Which class is this HW for?

11. Jan 30, 2007

### s4orce

It is for a dynamics class, I just want to get a head start on a set of problems that were given to me

12. Jan 30, 2007

### Cyrus

I think you need to review the basics of dynamics. What it means when they say acceleration, velocity, and position.

I think you need to solidify the fundamentals before doing this HW. You should know better that acceleration is the second derivative of position by now.

13. Jan 30, 2007

### s4orce

so you cant help me?

14. Jan 30, 2007

### Cyrus

Sure, tell me what the definition of acceleration is, and look for your mistake.

I can point out mistakes, but im not going to teach you fundamentals.

15. Jan 30, 2007

### s4orce

can you solve it and I can find my mistake, or post how.

also acceleration is the rate at which a object increases/changes its velocity(speed)

16. Jan 30, 2007

### Cyrus

Ah, Im sorry. Its asking for velocity as a function of position. I was thinking you had to integrate twice.

What you need to do: set up your limits of integration.

17. Jan 30, 2007

### s4orce

?????????????????

18. Jan 30, 2007

### Cyrus

Do you know what limits of integration are?

19. Jan 30, 2007

### s4orce

yes integral from one value to another

20. Jan 30, 2007

### Cyrus

so what are your value you used?