# Velocity and acceleration.

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!!

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## Answers and Replies

Tide
Science Advisor
Homework Helper
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?