# Point Particle Motion problem

1. Dec 3, 2008

### jackiemoon

Hi,

Can anybody help with the following:

A point particle moves in a plane with trajectory given by r(t) = R [θ (t)]^3/2, where R is a constant.

The angle θ in radians increases in time according to the equation θ (t) = 1/2 α t^2,
where α is a constant whose numerical value is α = 1 s^-2.

a. Sketch the trajectory of the particle.
b. Compute the time t > 0, if any, for which the radial and tangential components of the velocity of the particle coincide.
c. Compute the time t > 0, if any, for which the acceleration of the particle is purely tangential.
d. Compute the time t > 0, if any, for which the radial acceleration of the particle is twice its tangential acceleration.

I really am struggling with this question. I'm not even sure about sketching the trajectory, which is usually the least I can do in these type of questions! Can anybody help and explain it in really simple terms. Thanks for any help with this.

2. Dec 3, 2008

### LowlyPion

What you have is an equation in polar coordinates don't you?

And if |R| is constant, it is described how?