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**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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