Work the Following on Notebook Paper. Use Your Calculator on Problems 10 and 13C Only

CALCULUS BC

WORKSHEET 1 ON VECTORS

Work the following on notebook paper. Use your calculator on problems 10 and 13c only.

1. If

2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is , find its

velocity vector at time t = 2.

3. A particle moves in the xy-plane so that at any time t, its coordinates are given

by Find its acceleration vector at t = 1.

4. If a particle moves in the xy-plane so that at time t its position vector is find the velocity

vector at time

5. A particle moves on the curve so that its x-component has derivative At

time t = 0, the particle is at the point (1, 0). Find the position of the particle at time t = 1.

6. A particle moves in the xy-plane in such a way that its velocity vector is If the position vector

at t = 0 is, find the position of the particle at t = 2.

7. A particle moves along the curve ?

8. The position of a particle moving in the xy-plane is given by the parametric equations

For what value(s) of t is the particle at rest?

9. A curve C is defined by the parametric equations Write the equation of the line

tangent to the graph of C at the point

10. A particle moves in the xy-plane so that the position of the particle is given by

Find the velocity vector at the time when the particle’s horizontal position is x = 25.

11. The position of a particle at any time is given by

(a) Find the magnitude of the velocity vector at time t = 5.

(b) Find the total distance traveled by the particle from t = 0 to t = 5. (c) Find as a function of x.

12. Point moves in the xy-plane in such a way that

(a) Find the coordinates of P in terms of t given that t = 1, , and y = 0.

(b) Write an equation expressing y in terms of x.

(d) Find the instantaneous rate of change of y with respect to x when t = 1.

13. Consider the curve C given by the parametric equations

(a) Find as a function of t. (b) Find the equation of the tangent line at the point where

intercepts.

Answers to Worksheet 1 on Vectors

1. 2. 3. 4. 5. 6.

7. 8. t = 3 9.

10.

11. (a) (b) (c)

(d) 4

13. (a) (b) (c)

CALCULUS BC

WORKSHEET 2 ON VECTORS

Work the following on notebook paper. Use your calculator on problems 7 – 11 only.

1. If in terms of t.

2. Write an integral expression to represent the length of the path described by the parametric

equations

3. For what value(s) of t does the curve given by the parametric equations

have a vertical tangent?

4. For any time, if the position of a particle in the xy-plane is given by find

the acceleration vector.

5. Find the equation of the tangent line to the curve given by the parametric equations

at the point on the curve where t = 1.

6. If are the equations of the path of a particle moving in the xy-plane, write an

equation for the path of the particle in terms of x and y.

7. A particle moves in the xy-plane so that its position at any time t is given by

What is the speed of the particle when t = 2?

8. The position of a particle at time is given by the parametric equations

(a) Find the magnitude of the velocity vector at t = 1.

(b) Find the total distance traveled by the particle from t = 0 to t = 1.

9. An object moving along a curve in the xy-plane has position at time with

. Find the acceleration vector and the speed of the object when t = 5.

10. A particle moves in the xy-plane so that the position of the particle is given by

Find the velocity vector when the particle’s vertical position is y = 5.

11. An object moving along a curve in the xy-plane has position at time t with

and At time t = 1, the object is at the position (3, 4).

(a) Write an equation for the line tangent to the curve at (3, 4).

(b) Find the speed of the object at time t = 2.

(d) Find the position of the object at time t = 2.

12. A particle moving along a curve in the xy-plane has position at time t with

At time t = 1, the particle is at the position (5, 6).

(a) Find the speed of the object at time t = 2.

(b) Find the total distance traveled by the object over the time interval

(d) For , there is a point on the curve where the line tangent to the curve has slope 8. At what

time t, , is the particle at this point? Find the acceleration vector at this point.

Answers to Worksheet 2 on Vectors

1. 2.

5. 6.

7. 12.304

8. (a) (b) 3.816 (c) At rest when t = 2. Position = (4, 0)

9., speed = 28.083

(b) 2.084 (c) 1.126 (d) (3.436, 3.557)

12. (a) 1.975 (b) 1.683 (c) 7.661 (d) t = .752;