# Objects moving in a plane.

1. Sep 26, 2007

### crazy_shoes

I'm having terrible difficulty starting this problem, it's one of the chapter excercises in the book and it's revisited in the homework later on. I'm going to give different data, as I would like to actually solve this one myself, I just need a kick start...

1. The problem statement, all variables and given/known data
We've got an object moving in a plane, no velocity is stated at all, just that it's moving. It's mass is 6.00 kg and it's coordinates are given by 2 equations, $$x = 4t^2 - 1$$ and $$y = 2t^3 + 6$$. They are asking what the net force acting on this object is at time t = 5.00s.

2. Relevant equations
I know somewhere in there I'm going to use kinematic equations. I started by trying to find $$\Delta X$$ and $$\Delta Y$$...

Thanks to anyone who can point me in the right direction!

Last edited: Sep 26, 2007
2. Sep 26, 2007

### Avodyne

It's in a plane, so position, velocity, acceleration, and force are all vectors with x and y components. The position vector is (x,y)=(4t2-1,2t3+6). Can you find the velocity vector? (How is velocity related to position?) Then, can you find the acceleration vector? Then, can you find the force vector?

3. Sep 26, 2007

### crazy_shoes

Ah, that makes a lot of sense! Thank you so much! I was completely overlooking that.

4. Sep 26, 2007

### Avodyne

Glad to help.

5. Sep 26, 2007

### crazy_shoes

If I'm using position to get a velocity vector with the formula $$V_x_{avg} = \frac{\Delta x}{\Delta t}$$, can I use t = 0 for my $$t_i$$?

6. Sep 26, 2007

### Avodyne

You should be computing instantaneous velocity, not average velocity.

I assume this is a calculus-based course?

7. Sep 26, 2007

### crazy_shoes

For the formulas I have you still need $$\Delta x$$ and $$\Delta t$$

$$v_x = lim_{\Delta t \rightarrow 0}\frac{\Delta x}{\Delta t}$$

...and yes, this is calculus based.

I feel like I've missed a lesson or missed something in class.

8. Sep 26, 2007

### Avodyne

That limit defines the derivative of x with respect to t. Given x as a simple function of t, say, x=t2, can you compute the derivative dx/dt ?

9. Sep 26, 2007

### crazy_shoes

OH! So it would be 2t then... If the function was in fact $$t^2$$.

10. Sep 26, 2007

### meopemuk

You would need two formulas:

1. Newton's second law $\mathbf{F} = m \mathbf{a}$ and
2. definition of components of the acceleration vector

$$a_x = d^2x(t)/dt^2$$
$$a_y = d^2y(t)/dt^2$$

Eugene

11. Sep 26, 2007

### crazy_shoes

So, if my position in the x direction is a function of time, like $$x=2t^2$$ the derivative of that is $$4t$$ which should be my velocity in the x direction. Then a second derivative should give me 4 and that should be my acceleration in the x direction. Am I on the right track?

12. Sep 26, 2007

### meopemuk

Yes, you got it.

Eugene.

13. Sep 26, 2007

### crazy_shoes

Thanks! It's much appreciated. Good thing I have a whole week to finish studying for my test!

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