Given rt cos t sin t tfind the velocity acceleration and sp

Given r(t) = cos t, sin t, t,find the velocity, acceleration and speed at t = pi/2.

Solution

Velocity is given by r\'

r\'=<-sin(t),cos(t),1>

At t=pi/2 it takes teh value

r\'=<-1,0,1>

Acceleration is given by r\'\'

r\'\'=<-cos(t),-sin(t),0>

At t=pi/2 it takes the value

r\'\'=<0,-1,0>