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Stewart_Calc_7ET ch13sec04
MULTIPLE CHOICE
1. A particle moves with position function .
Find the tangential component of the acceleration vector.
a.
b.
c.
d.
e.
2. A force with magnitude N acts directly upward from the xy-plane on an object with mass
kg. The object starts at the origin with initial velocity . Find its position
function.
a.
b.
c.
d.
e.
3. Find the acceleration of a particle with the following position function.
a.
b.
c.
d.
e.
4. Find the velocity of a particle with the given position function.
3
a.
b.
c.
d.
e.
5. Find the acceleration of a particle with the given position function.
a.
b.
c.
d.
e.
6. Find the speed of a particle with the given position function.
a.
b.
c.
d.
e.
7. Find the velocity of a particle that has the given acceleration and the given initial velocity.
a.
b.
c.
d.
e.
8. The position function of a particle is given by
When is the speed a minimum?
a.
b.
c.
d.
e.
9. A mortar shell is fired with a muzzle speed of 325 ft/sec. Find the angle of elevation of the
mortar if the shell strikes a target located 1500 ft away. Round your answer to 2 decimal
places.
a.
b.
c.
d.
10. Find the scalar tangential and normal components of acceleration of a particle with position
vector
a.
b.
c.
d.
11. Find the scalar tangential and normal components of acceleration of a particle with position
vector
a.
,
b.
,
c.
,
d.
,
12. What force is required so that a particle of mass has the following position function?.
a.
b.
c.
d.
e.
13. A projectile is fired with an initial speed of and angle of elevation . Find the
range of the projectile.
a.
km
b.
km
c.
km
d.
km
e.
km
14. Find the speed of a particle with the given position function.
a.
b.
c.
d.
e.
15. A ball is thrown at an angle of to the ground. If the ball lands m away, what was the
initial speed of the ball? Let .
a.
b.
c.
d.
e.
16. The following table gives coordinates of a particle moving through space along a smooth
curve.
Find the average velocity over the time interval .
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. A particle moves with position function . Find the acceleration of
the particle.
2. A particle moves with position function .
Find the normal component of the acceleration vector.
3. Find the position vector of a particle that has the given acceleration and the given initial
velocity and position.
SHORT ANSWER
1. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration
vectors.
2. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration
vectors.
3. Find the unit tangent and unit normal vectors and for the curve C defined by
Sketch the graph of C, and show and for
4. Find the unit tangent and unit normal vectors and for the curve C defined by
5. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration
vectors.
6. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration
vectors.
7. Find the scalar tangential and normal components of acceleration of a particle with position
vector
8. A projectile is fired from a height of 400 ft with an initial speed of 200 ft/sec and an angle of
elevation of .
a. What are the scalar tangential and normal components of acceleration of the projectile?
b. What are the scalar tangential and normal components of acceleration of the projectile
when the projectile is at its maximum height?
9. Find the velocity, acceleration, and speed of an object with position vector
.
10. Find the velocity, acceleration, and speed of an object with position vector
.
11. Find the velocity and position vectors of an object with acceleration
initial velocity and initial position
12. A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of
elevation of
a. Find the range of the projectile.
b. What is the maximm height attained by the projectile?
c. What is the speed of the projectile at impact?
Round your answers to the nearest integer.
