AP Calc Bc 2024 Ap test Q #2

A particle moving along a curve in the xy-plane has position ( () x t , y t( )) at time t seconds, where x t( ) and y t( )
are measured in centimeters. It is known that x t 8t t
2 ¢( ) = − and y t t t 20 1.2 ¢ = ( ) − + + . At time t = 2
seconds, the particle is at the point (3, 6).
(a) Find the speed of the particle at time t = 2 seconds. Show the setup for your calculations.
(b) Find the total distance traveled by the particle over the time interval 0 £ £t 2. Show the setup for your
calculations.
(c) Find the y-coordinate of the position of the particle at the time t = 0. Show the setup for your calculations.
(d) For 2 £ £t 8, the particle remains in the first quadrant. Find all times t in the interval 2 £ £t 8 when the
particle is moving toward the x-axis. Give a reason for your answer.