A car moves on a circle of constant radius b. The speed of the car varies with time according to the equation, v = ct, where c is a positive constant.
a) Draw a diagram showing the direction of the velocity and acceleration(s). Find the velocity and acceleration vectors (Directions of the vectors you have chosen to show in your diagram).
b)Find the angle between the velocity vector and the acceleration vector. (Note: Express the angle in terms of c and t)
2. Relevant equations
V = dx/dt
A = dv/dt
3. The attempt at a solution
Position Vector (from center of circle): b cos (u(t))i +b sin(u(t))j;
u(t) = a function of time
Velocity vector: -b u`cos(u(t))i + b u` sin(u(t))j;
bu`(t) = ct
u(t) = 1/2 (c/b)t^2
Velocity Vector: -(c)(t)sin(1/2(c/b)t^2)i+(c)(t)cos(1/2(c/b)t^2)j
Acceleration Vector: (c-(c^2 t^2)/b)cos(1/2(c/b)t^2)i+((-c^2 t^2)/b-c)sin(1/2(c/b)t^2)j
I’m not sure if I did this correct. If not can you please show me my error and help with part b? 🙂