# B Path of a particle.

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1. Mar 31, 2016

### LoveBoy

Hi There.
I want to ask a question, here it is :-

How to find the path of a particle if initial velocity(vector) is given and constant force(vector) acts on the particle.

Like :-
1) How can we determine the path will be PARABOLIC
2) How can we determine the path will be CIRCULAR.
3) How can we determine the path will be STRAIGHT LINE.

If you don't understand , i'll post the question if necessary.

2. Mar 31, 2016

### PeroK

If you want help with a specific problem, you should post it in the homework section.

In general, you determine the path of a particle by solving the equation(s) of motion.

3. Mar 31, 2016

### LoveBoy

That is my question ?
How do we solve it if initial velocity vector is given and constant force(vector) is given ?

4. Mar 31, 2016

### ZapperZ

Staff Emeritus
You use one of the kinematical equations!

If this is from a school work, you should already know about these kinematical equations. In any case, this is too vague. Pick a specific problem you are having trouble with, attempt as much as you can, and then post in the HW forum. Otherwise, you'll get vague answers to accompany your vague questions.

Zz.

5. Mar 31, 2016

### PeroK

You have one vector equation, which is equivalent to three equations, one for each spatial dimension:

$\vec{r} = \vec{r}_0 + \vec{v}_0 t + \frac{1}{2} \vec{a} t^2$

Or:

$x = x_0 + v_{0x} + \frac{1}{2}a_xt^2, \ \ y = y_0 + v_{0y} + \frac{1}{2} a_yt^2, \ \ z = z_0 + v_{0z} + \frac{1}{2} a_zt^2$

Finding the shape of the path then depends on finding a relationship between $x, y$ and $z$.

You should try some examples in two dimensions.

6. Mar 31, 2016

### LoveBoy

Thanks for posting.
But i don't understand it well.

I'll post a question in HW section .
Thanks again !

7. Apr 3, 2016

### hackhard

init velocity vector = P const force vector = Q
if in frame A ,P is non parallel and non antiparallel to Q -- parabolic path in frame A
if Q is const in frame A, then circular motion impossible in frame A
if only mag of Q const , then ---
if (|P|^2) / (proj of instantaneous Q vector along normal to P) = const ---- circular motion
Q parallel or anti parallel to P --straight line