Chapter 2
Kinematics in One Dimension
Kinematics deals with the concepts that
are needed to describe motion.
Dynamics deals with the effect that forces
have on motion.
Together, kinematics and dynamics form
the branch of physics known as Mechanics.
2.1 Displacement

x o  initial
position

x  final position
  
 x  x  x o  displaceme
nt
2.2 Speed and Velocity
Average speed is the distance traveled divided by the time
required to cover the distance.
Average
speed 
Distance
Elapsed
time
SI units for speed: meters per second (m/s)
2.2 Speed and Velocity
Average velocity is the displacement divided by the elapsed
time.
Average
velocity

Displaceme
Elapsed

v
 
x  xo
t  to

nt
time

x
t
2.2 Speed and Velocity
The instantaneous velocity indicates how fast
the car moves and the direction of motion at each
instant of time.

v  lim
t  0

x
t
2.3 Acceleration
DEFINITION OF AVERAGE ACCELERATION

a 
 
v  vo
t  to


v
t
2.4 Equations of Kinematics for Constant Acceleration
Five kinematic variables:
1. displacement, x
2. acceleration (constant), a
3. final velocity (at time t), v
4. initial velocity, vo
5. elapsed time, t
2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
v  v o  at
x
1
2
v o  v  t
v  v  2 ax
2
2
o
x  vot 
1
2
at
2
2.6 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. If the distance of the fall is small
compared to the radius of the Earth, then the acceleration
remains essentially constant throughout the descent.
This idealized motion is called free-fall and the acceleration
of a freely falling body is called the acceleration due to
gravity.
g  9 . 80 m s
2
or
32 . 2 ft s
2
2.6 Freely Falling Bodies
g  9 . 80 m s
2
Example 2.1
• You are driving your new sports car at a
velocity of 90km/h, when you suddenly
see a dog step into the road 50m ahead.
You hit the brakes hard to get maximum
deceleration of 7.5m/s2. How far will you
go before stopping? Can you avoid hitting
the dog?
Solution
• By definition, we have
v2 = vo2 + 2ax
x = [v2 – v02 ]/[2a]
= [(0)2 – (25)2]/[2×(-7.5)]
= 41.67m
Fortunately, you are able to stop without hitting
the dog.
NB: 90km/h = 25m/s
Problems to be solved
• 2.10, 2.29, 2.40, 2.49. 2.76
• B2.1: A car moving at 15m/s hits a stone
wall. (a) A seat-belted passenger comes
to rest in 1m. What acceleration does this
person experience? (b) Another
passenger without a seat belt strikes the
windshield and comes to rest in 0.01m.
What acceleration does this person
experience?
• B2.2: A boy standing beside a tall building
throws a ball straight up with an initial
velocity of 15m/s. (a) How high will the ball
rise? (b) How long will it take for the ball to
reach its maximum height? (c) Another
boy reaches out of a window 6m above
the initial position of the ball and attempts
to catch the ball. At what times will the ball
pass him?
• B2.3: The hammer of a pile driver strikes
the top of a pipe with a velocity of 7m/s.
From what height did the hammer fall?
• B2.4: A physics student measures her reaction
time by having a friend drop a metre stick
between her fingers. The metre stick falls 0.3m
before she catches it. (a) What is her reaction
time? (b) Estimate the minimum speed of nerve
impulses going from her eye to her brain and
then back to her hand. [Assumptions: eye to
brain distance=3cm. Brain to hand distance =
75cm.]