# Velocity and acceleration.

1. Oct 4, 2005

### fahd

velocity & acceleration PLZZZZ HELP ME!

hi i have this question from fowles anlaytical mechanics.It says

A racing car moves along a circular track of radius 'a'.The speed of the car varies with time as v=kt where k is a poistive constant.Show that the angle between the velocity vector and acceleration vector is 45 degrees when t= (a/k)^1/2

i took the equation of motion to be r= a cos[(kt^2)/a]+a sin[(kt^2)/a]
then differentiated to get velocity and acceleration...i represented a particular portion of each velocity and acceleration as a unit vector p and q so as to reduce the size of the equations.HOwever when i try to calculate the angle between a and v..at that time..it doesnt come out to be 45..Can ne one please help ,me!!

Last edited: Oct 4, 2005
2. Oct 5, 2005

### Tide

You can determine both the tangential and radial (centripetal) components of velocity and acceleration at any instant. Make it easy on yourself and choose your coordinates for a given instant of time to be such that the tangential direction is, say, in the postitive y direction and the radial component in the x direction.

Then note that $\vec v \cdot \vec a = v a \cos \theta$ and you can explicitly evaluate the dot product since you know the components of each vector. What must t be in order for $\theta$ to be 45 degrees?