# Look of trajectory of a material point

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1. Oct 8, 2014

### Chemist@

1. The problem statement, all variables and given/known data
A body is moving, with the following data (these are all dependencies of the radius vector components respective to time): x(t)=At2, A>0; y(t)=Bt, B>0, z(t)=0. How does the trajectory of this movement look?

2. Relevant equations
r=x(t)i+y(t)j+z(t)k
Velocity=dr/dt
3. The attempt at a solution
r=At2*i+Bt*j (i,j and r are vectors)
Velocity=2At*i+B*j
Intuitively I think that the trajectory would look like a logarithm function, but is it correct and how to prove it?

2. Oct 8, 2014

### Staff: Mentor

Since z(t)=0 for all t the trajectory must lie entirely in the x-y plane. Did you try to sketch the trajectory? Pick arbitrary values for A and B and plot a few points. Alternatively, find y as a function of x and comment on the type of function it represents.

3. Oct 8, 2014

### nasu

You may know already a type of motion which satisfies similar conditions.

4. Oct 8, 2014

### Chemist@

I thought that it would look similar to y=log(x). Correct?

5. Oct 8, 2014

### Staff: Mentor

Similar it may be, but you can find the actual equation by converting from parametric form to standard y(x) = ... form.

6. Oct 8, 2014

### Chemist@

Is it y=B*sqrt(x/A)?

7. Oct 8, 2014

### Staff: Mentor

Yup. Or if you combine the constants, $y = c\sqrt{x}$ .