# Thread: particle motion and parametics

1. ## particle motion and parametics

a particle moving in a plane has position at time t given by
x(t) = (2 cos t, sin (2t)) , 0<=t<=Pi

(a) find the position and velocity of the particle at times
t=0, t=(pi/2) and t=pi

(b) find the vector equation of the tangent line to the path of the particle at
t0 = (pi/4)

(c) make a sketch of the path of the particle for 0<=t<=Pi, indicating the relevant positions and velocities from parts (a) and (b) above
(hint: draw the component curves)

2. Originally Posted by razorfever
a particle moving in a plane has position at time t given by
x(t) = (2 cos t, sin (2t)) , 0<=t<=Pi

(a) find the position and velocity of the particle at times
t=0, t=(pi/2) and t=pi
Hint: velocity is given by v(t) = x'(t)

(b) find the vector equation of the tangent line to the path of the particle at
t0 = (pi/4)
this is given by $L = x \left( \frac {\pi}4 \right) + t \cdot v \left( \frac {\pi}4 \right)$

note, write x(t) as a point and v(t) as a vector

(c) make a sketch of the path of the particle for 0<=t<=Pi, indicating the relevant positions and velocities from parts (a) and (b) above
(hint: draw the component curves)
do this by plotting some points. use parts (a) and (b) to help