Look of trajectory of a material point

[Chemist@]

Homework Statement

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?

Homework Equations

r=x(t)i+y(t)j+z(t)k
Velocity=dr/dt

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?

 

[gneill]

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.

 

[nasu]

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

 

[Chemist@]

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

 

[gneill]

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

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

 

[Chemist@]

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

 

[gneill]

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

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