The position vector of a particle is r = a t i + a t j . Calculate the angle between its position vector and the velocity vector. ( 0=1, 90=0, 60=0.5, 30=0.5, 0=0 )

Step-by-step solution

Given position vector r = a t i + a t j Velocity vector v = d r dt = -a t i + a t j The dot product of r and v is: r v = (a t)(-a t) + (a t)(a t) r v = -a^2 t t + a^2 t t = 0 Since r v = 0 , the angle between the position vector and the velocity vector is 90^ .