Physics for Dentistry and
Medicine students
PHYS 145
Text book
Physics; John D. Cutnell and Kenneth W.
Johnson; 7th edition; Wiley; 2007.
Chapter 2
Kinematics in One
Dimension
As this barn owl comes in for a landing, it is slowing down while moving forward.
To describe such motion, this chapter presents the concepts of displacement,
velocity, and acceleration. (Manfred Danegger/Photo Researchers, Inc.)
Displacement and Distance
• Definition: The displacement is a vector
that points from an object’s initial position to
its final position and has a magnitude that
equals the shortest distance between the two
positions.
• SI Unit of Displacement: meter (m)
Speed and Velocity
• Average Speed
Distance
Average speed 
Elapsedtim e
• Definition of Average Velocity
Displacement
Average velocity
Elapsedtim e
 

 x  xo  x
v

t  to  t
• SI Unit of Average Velocity and Speed:
meter per second (m/s)
Instantaneous Velocity
• The instantaneous velocity v of the car
indicates how fast the car moves and the
direction of the motion at each instant of
time. The magnitude of the instantaneous
velocity is called the instantaneous
speed, and it is the number (with units)
indicated by the speedometer


x
v  lim
t 0  t
Acceleration
• Definition of Average Acceleration
Change in velocity
Average acceleration 
Elapsedtim e
 

 v  vo  v
a

t  to
t
SI Unit of Average Acceleration: (m/s2)
• The instantaneous acceleration


v
a  lim
t 0  t
Equations of Kinematics for
Constant Acceleration
Equation
v = vo + at
x = ½ (vo +v) t
x = vot + ½ at2
v2 = vo2 + 2ax
x
-
a
Variable
v
vo
t
-
Freely Falling Bodies
• In the absence of air resistance, it is found
that all bodies at the same location above
the earth fall vertically with the same
acceleration.
• The acceleration of a freely falling body is
called the acceleration due to gravity g
g = 9.80 m/s2 or 32.2 ft/s2
Demo
(a) In the presence of
air resistance, the
acceleration of the
rock is greater than
that of the paper.
(b) In the absence of
air resistance, both the
rock and the paper
have the same
acceleration.
Example
• A stone is dropped
from rest from the top
of a tall building, as
the figure indicates.
After 3.00 s of freefall, what is the
displacement y of the
stone?
Graphical Analysis of Velocity
and Acceleration
• A graph of position vs. time for an object moving
with a constant velocity of v = Slope = Δx/Δt =
+8m/ +2s = +4 m/s.
Example 16: A Bicycle Trip
A velocity vs. time graph that applies to an object
with an acceleration of a = Slope = Δv/Δt =
+12m.s-1/ +2s = +6 m/s2.
The initial velocity is vo = +5 m/s when t = 0 s.
Problems
1/203) A whale swims due east for a
distance of 6.9 km, turns around and goes
due west for 1.8 km, and finally turns
around again and heads 3.7 km due east.
(a) What is the total distance traveled by
the whale? (b) What are the magnitude
and direction of the displacement of the
whale?
Solution: a) 12.4 km.
b) 8.8 km due east.
Problems
2/203)
You step onto a hot beach with
your bare feet. A nerve impulse, generated
in your foot, travels through your nervous
system at an average speed of 110 m/s.
How much time does it take for the
impulse, which travels a distance of 1.8 m,
to reach your brain?
Solution:
x = ½ (vo +v) t
1.8 m = 110 m/s t
t = 0.016 s
Solve This Problem
19/205) In getting ready to slam-dunk
the ball, a basketball player starts
from rest and sprints to a speed of 6.0
m/s in 1.5 s. Assuming that the player
accelerates uniformly, determine the
distance he runs.
Problems
• 32/206) The left ventricle of the heart
accelerates blood from rest to a velocity of
+26 cm/s. (a) If the displacement of the blood
during the acceleration is +2.0 cm, determine
its acceleration (in cm/s2). (b) How much time
does blood take to reach its final velocity?
Solution: a) v2 = vo2 + 2ax
(26)2 = 0 + 2 (a) 2.0 cm
a = 169 cm/s2
b) v = vo + at
26 = 0 + 169 t
t = 0.15 s
Problems
37/208) The greatest height reported for a
jump into an airbag is 99.4 m by stuntman
Dan Koko. In 1948 he jumped from rest from
the top of the Vegas World Hotel and Casino.
He struck the airbag at a speed of 39 m/s. To
assess the effects of air resistance,
determine how fast he would have been
traveling on impact had air resistance been
absent.
Solution: a) v2 = vo2 + 2ax
(v)2 = 0 + 2 (-9.8) (- 99.4 m)
v = 44.13 m/s
H.W.
• 41/210) A wrecking ball is hanging at
rest from a crane when suddenly the
cable breaks. The time it takes for the ball
to fall halfway to the ground is 1.2 s. Find
the time it takes for the ball to fall from
rest all the way to the ground.
Problems
57/211) A
snowmobile moves
according to the
velocity–time graph
shown in the drawing.
What is the
snowmobile’s
average acceleration
during each of the
segments A, B, and
C?
Problems
58/212)
A person who
walks for exercise produces
the position–time graph given
with this problem. (a) Without
doing any calculations, decide
which segments of the graph
(A, B, C, or D) indicate +ve,
-ve, and zero average
velocities. (b) Calculate the
average velocity for each
segment to verify your
answers to part (a).