Non-Textbook Problems
A. (i) Explain the difference between velocity and acceleration. (ii)
If an object travels with a constant velocity, what do we know about its
acceleration?
B. Match each of the following statements will one or more of the equations
of kinematics in one dimension (p. 38):
(i) The final velocity of an object experiencing constant acceleration
depends upon the initial velocity and the acceleration.
(ii) The displacement of an object experiencing constant acceleration
is equal to the average velocity of the object times the time elapsed.
(iii) If the displacement of an object experiencing constant acceleration
is plotted versus time, the function is parabolic, with the exact shape
determined by the initial velocity and the acceleration.
C. For the case of projectile motion, derive an equation expressing
the vertical displacement, y, as a function of: the horizontal displacement,
x; the acceleration due to gravity, g; and the x and y components of the
initial velocity. (HINT: Which variable do x and y have in common?) Graph
this function assuming that the x and y components of the initial velocity
are positive.
Textbook Problems, Chapter 3
Conceptual Questions (p. 77): 7, 10
Problems (p. 78): 13, 17, 67 |
Non-Textbook Problems
A. (i) The velocity of an object includes its speed and direction.
Acceleration is the change in velocity. (ii) If velocity is constant, acceleration
is 0.
B. (i) v=vo+at and v2=vo2+2ax
(ii) x=(1/2)(vo+v)t (iii) x=vot+(1/2)at2
C. y = (-g/(2vox2))x2 + (voy/vox)x
This parabola opens down, crosses the x-axis at 0 and 2voxvoy/g,
and has a vertex at (voxvoy/g, voy2/(2g)).
Textbook Problems, Chapter 3
Conceptual Questions
7. Yes. If the boat is at rest, the wrench falls directly below where
it was dropped. If the boat is moving with constant velocity, the wrench
is given a velocity in the x direction, but takes the same time to fall
as before. Its movement in the x direction exactly matches the boat's movement,
so it hits in the same place. (I've ignored air resistance.)
10. (a) Displacement is different. The stone that is thrown includes
both an x and y component of displacement, so total displacement is larger.
(b) Speed just before impact is different. The stone that is thrown
includes both x and y components of velocity, so impact speed will be greater.
(c) Time of flight is the same. It depends only on the y component
of the motion, which is the same for the two cases.
Problems
13. 4.4 s
17. 14.1 m/s
67. 15.7 degrees |