At time t, a particle moving in the xy-plane is at position ( ) x t y t ( ) ( ) , , where x t( ) and y( )t are not explicitly
given. For t ≥ 0, 4 1
dx
t
dt
= + and ( )
2
sin .
dy
t
dt
= At time t = 0, x( )0 0 = and y( )0 4. = -
(a) Find the speed of the particle at time t = 3, and find the acceleration vector of the particle at time t = 3.
(b) Find the slope of the line tangent to the path of the particle at time t = 3.
(c) Find the position of the particle at time t = 3.
(d) Find the total distance traveled by the particle over the time interval 0 3

Question

At time  t, a particle moving in the xy-plane is at position  ( ) x t  y t ( )  ( ) , , where  x t( ) and  y( )t are not explicitly 
given. For  t ≥ 0, 4 1
dx
t
dt
= + and  ( )
2
sin .
dy
t
dt
= At time  t = 0, x( )0 0 = and  y( )0 4. = -
(a) Find the speed of the particle at time  t = 3, and find the acceleration vector of the particle at time  t = 3.
(b) Find the slope of the line tangent to the path of the particle at time  t = 3.
(c) Find the position of the particle at time  t = 3.
(d) Find the total distance traveled by the particle over the time interval  0 3

dumbcow · Answer

could you rewrite the equations, hard to make them out