Two-Dimensional Motion of a Particle: Velocity & Acceleration

[chart2006]

Homework Statement

The two-dimensional motion of a particle is defined by the relationship r = \frac {1}{sin\theta - cos\theta} and tan\theta = 1 + \frac {1}{t^2}, where r and \theta are expressed in meters and radians, respectively, and t is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.

Homework Equations

r = \frac {1}{sin\theta - cos\theta}


tan\theta = 1 + \frac {1}{t^2}

The Attempt at a Solution

I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve tan\theta for \theta. Once I've done that I figure I'd need to differentiate both r and \theta to find \dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}.

I don't know if I'm on the correct route but any help would be appreciated. thanks!

 

[gabbagabbahey]

I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve tan\theta for \theta.

Tangent is not a one-to-one function, so that's a bad idea.

Instead, draw a picture! I think you can find expressions for \sin\theta and \cos\theta in terms of t without actually solving for \theta first...think 'right triangle'