Question

The position vector r(r)of a particle is given by r(t) = <3sin2t,3cos2t,2t>.Find its velocity v and acceleration a. show that the acceleration is orthogonal to the velocity.​

Answer 1

Hi,

Explanation:

r(t)=(x(t),y(t),z(t))=(3sin(2t),3cos(2t),2t)

v(t)=(dx/dt,dy/dt,dz/dt)=( 6cos(2t),-6sin(2t),2)

a(t)=dv/dt=(-12sin(2t),-12cos(2t),0)

dot product : a(t).v(t)=(-12sin(2t),-12cos(2t),0) . (6cos(2t),-6sin(2t),2)

=-72sin(2t)cos(2t)+72sin(2t)cos(2t)+0=0