The position of particle at time t is given by r rightarrowt

The position of particle at time t is given by r rightarrow(t) = lessthan 3, cos(t), sin(t) Greaterthan, Find the velocity and acceleration at time t.

Solution

Given that

r( t ) = < 3 , cos(t) , sin(t) >

The velocity of the particle at time t is ,

V(t) = r\'(t) = d/dt( r(t) )

V(t) = < 0 , - sin(t) , cos(t) > [ since, d/dt(cost) = - sint,

  ,d/dt(sint) = cost ]

The acceleration of particle at time t is ,

V(t) = < 0 , - sin(t) , cos(t) >

A(t) = r\'\'(t) = V\'(t) = d/dt( V(t) )

   A(t) = < 0 , - cos(t) , - sin(t) >   

Therefore,

Velocity at time t is , V(t) = < 0 , - sin(t) , cos(t) >

Acceleration at time t is ,   A(t) = < 0 , - cos(t) , - sin(t) >