# Calculating the velocity given the position of the particle

1. Aug 23, 2016

### TheLil'Turkey

1. The problem statement, all variables and given/known data
A particle moves with constant velocity along the curve r = e^(θ) and z = r (cylindrical coordinates). The speed, v, is constant.

a) Calculate the velocity and acceleration of the particle in terms of θ and v.

b) Show that the velocity and acceleration are perpendicular.

c) Find the expression for θ(t).

2. Relevant equations
v
= dr/dt (radial direction) + r dθ/dt (tangential direction)

v^2 = (dr/dt)^2 + r^2 (dθ/dt)^2 = constant

dr/dt = dr/dθ dθ/dt

3. The attempt at a solution

2. Aug 23, 2016

### haruspex

That's for 2 dimensions. This is moving in three.

Posting your algebra as an image makes it hard to refer to specific equations in comments.

Expressing dr/dt in terms of dθ/dt, then expressing that in terms of dr/dt is going round in circles. Get all the velocity components expressed in terms of the time derivative of one of the coordinates - r, θ, or z, whichever is easiest - as you eventually did.