The position vector `vecr` of a particle with respect to the origin changes with time t as `vecr =Athati-Bt^2hatj,` where A and B are positive constants. Determine
(ii) the nature of variation with time of the velocity and acceleration vectors, and also the moduli of them.

Explanation

Velocity, `vecv=(vec(dr))/(dt)=Ahati-2Bthatj`
Its modulus. `|vecv|=sqrt(A^2+(-2Bt)^2)=sqrt(A^2+4B^2t^2)`
Acceleration , `veca=(vec(dv))/(dt)=-2Bhatj`
its modulus, `|veca|=sqrt((-2B)^2)=2B`