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CALCULUS BC WORKSHEET 3 ON VECTORS

calculus bc worksheet 3 on vectors work the following on notebook paper. use your calculator only on problems 3 – 7. 1. t
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CALCULUS BC
WORKSHEET 3 ON VECTORS
Work the following on notebook paper. Use your calculator only on
problems 3 – 7.
1. The position of a particle at any time t 0 is given by

(a) Find the magnitude of the velocity vector at t 2.
(b) Set up an integral expression to find the total distance traveled
by the particle from t 0 to t 4.
(c) Find as a function of x.
(d) At what time t is the particle on the yaxis? Find the
acceleration vector at this time.
2. An object moving along a curve in the xyplane has position
at time t with the velocity vector
At time t 1, the object is at (ln 2, 4).
(a) Find the position vector.
(b) Write an equation for the line tangent to the curve when t 1.
(c) Find the magnitude of the velocity vector when t 1.
(d) At what time t > 0 does the line tangent to the particle at
have a slope of 12?
3. A particle moving along a curve in the xyplane has position
, with and
Find the velocity vector at the time when the particle’s
vertical
position is y 7.
4. A particle moving along a curve in the xyplane has position
at time t with .
The derivative is not explicitly given. At time t 2, the
object is at position .
(a) Find the xcoordinate of the position at time t 3.
(b) For any t 0, the line tangent to the curve at has a
slope of t + 3. Find the acceleration
vector of the object at time t 2.
5. An object moving along a curve in the xyplane has position
at time t with
At time t 1, the object is at the point (3, 2).
(a) Find the equation of the tangent line to the curve at the point
where t 1.
(b) Find the speed of the object at t 1.
(c) Find the total distance traveled by the object over the time
interval
(d) Find the position of the object at time t 2.
6. A particle moving along a curve in the xyplane has position
at time t with
At time t 2, the particle is at the point (5, 3).
(a) Find the acceleration vector for the particle at t 2.
(b) Find the equation of the tangent line to the curve at the point
where t 2.
(c) Find the magnitude of the velocity vector at t 2.
(d) Find the position of the particle at time t 1.
TURN>>>
7. An object moving along a curve in the xyplane has position
at time t with
The derivative is not explicitly given. At t 3, the object
is at the point (4, 5).
(a) Find the ycoordinate of the position at time t 1.
(b) At time t 3, the value of is Find the value of
when t 3.
(c) Find the speed of the object at time t 3.
Answers to Worksheet 3 on Vectors
1. (a) Magnitude (b) Distance
(c) (d) Particle is on the yaxis when .

(b) (c) Magnitude
(d)
3.
4. (a)
(b)
5. (a) When t 1,
(b) Speed 1 (c) Distance 2
so position (2.896, 1.676)
6. (a)
(b)
(c) Magnitude 3.750
. Position (2.239, 1.664)
7. (a) 1.269
(b)
(c) Speed 3.36

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