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PREMEDICAL COURSE – PHYSICS
2. KINETICS
PREMEDICAL COURSE – PHYSICS
2. Kinetics: Motion on a straight line. Velocity, acceleration. Freely falling bodies
Veronika Kollár - University of Pécs, Medical School, Department of Biophysics, 2014 August
OVERVIEW
Introduction
Distance and displacement
Speed and velocity
Acceleration
The types of the linear motion
Free fall
INTRODUCTION
Kinetics describes the motion of objects using diagrams, numbers, graphs, and equations. Kinematics
is a branch of mechanics. The goal of any study of kinematics is to develop sophisticated mental
models that serve to describe the motion of real-world objects. The motion of objects can be
described by words. Even a person without a background in physics has a collection of words that can
be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down,
speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In
physics, we use these words and many more such as distance, displacement, speed, velocity, and
acceleration.
DISTANCE AND DISPLACEMENT
The way - the points in which the body is moving under the given time (the trajectory of motion).
The distance - is how much ground is covered by an object, regardless of its starting or ending
position. There is no directional component to a distance measurement, making it a scalar quantity.
It is representing the interval between two points.
E.g. So during my training I ran 1 kilometers total. It doesn't matter where the starting line or finish
line were or in which direction I was running. It only matters that, if you trace and measure my path, I
covered a distance of 1 km of ground. So, when we asked the other runners how far I had traveled,
they all answered correctly with a distance measurement of 1 kilometers.
The displacement - is a vector quantity that refers to "how far out of place an object is"; it is the
object's overall change in position.
Example 1
Look at the picture above, boy travels from A to B, B to C, C to D and D to A. The total distance is
1000 m (1 km). Yet when he is finished walking, she is not "out of place" - i.e., there is no
displacement for her motion (displacement = 0 m). So The displacement from A to A (which are our
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PREMEDICAL COURSE – PHYSICS
2. KINETICS
initial and final points) is zero. The 400 meters east cancels the 400 meters west; and the 100 meters
south cancels the 100 meters north.
A
400 m
100 m
D
B
100 m
400 m
C
SPEED AND VELOCITY
Speed – is a scalar quantity that refers to “how fast an object is moving”.
A fast-moving object has a high speed and covers a relatively large distance in a short amount of
time. Contrast this to a slow-moving object that has a low speed; it covers a relatively small amount
of distance in the same amount of time.
Velocity - is a vector quantity that refers to "the rate at which an object changes its position."
Imagine a person moving rapidly - one step forward and one step back - always returning to the
original starting position. The velocity is zero. Because the person always returns to the original
position, the motion would never result in a change in position. When evaluating the velocity of an
object it would not be enough to say that an object has a velocity of 20 miles/hr. One must include
direction information in order to fully describe the velocity of the object. For instance, you must
describe an object's velocity as being 20 miles/hr, west. This is one of the essential differences
between speed and velocity.
Average speed, average velocity, instantaneous speed
Instantaneous speed: During a trip the bus will undergo a series of changes in its speed. The
speedometer of a bus reveals information about the instantaneous speed of your car. It shows your
speed at a particular instant in time.
Example 2
The boy walks 400 m East, 100 m South, 400 West and
100 m North. The entire motion took for 12 minutes
(720 s). Determine the average speed and the average
velocity. He walked a distance of 1000 m; thus his
average speed is 1000 m/720 s= 1.39 m/s. However his
displacement is 0 m, his average velocity is 0 m/s.
A
400 m
100 m
D
B
100 m
400 m
C
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PREMEDICAL COURSE – PHYSICS
2. KINETICS
ACCELERATION
Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An
object is accelerating if it is changing its velocity.
Acceleration has to do with changing how fast an object is moving. If an object is not changing its
velocity, then the object is not accelerating.
Average acceleration
a average 
v  m 
 
t  s 2 
The acceleration is a vector quantity, it has a direction. The direction of the acceleration vector
depends on two things:
whether the object is speeding up or slowing down
whether the object is moving in the + or - direction
If an object is slowing down, then its acceleration is in the opposite direction of its motion.
Example 3
Determine the acceleration of the runner. Use the data at the below.
Motion A
Time (s)
Velocity (m/s)
0
0
2
3
4
6
8
9
Motion B
Time (s)
Velocity (m/s)
0
12
2
8
4
4
8
0
Answer A:
Answer B:
Δv=9-0=9 m/s
Δv=0-12=- 12 m/s
Δt=8 s
a=9/8= 1.125 m/s2
Δt=8 s
a=-12/8= -1.359 m/s2
THE TYPES OF THE LINEAR MOTION
1) Uniform motion
The body is moving
− in a straight line path.
− the direction of its movement does not change.
− it runs same lengths under the uniform time (constant speed/velocity).
− acceleration is zero.
The velocity of the uniform motion:
v
d  d0
t  t0
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PREMEDICAL COURSE – PHYSICS
2. KINETICS
It is determined by two parameters:
1. starting place: d0, (generally kept zero)
2. velocity: v
d  d0  v  t
Distance – time graph:
Geometrically: the velocity is the slope of the length-time curve.
v
d
 tg
t
Velocity – time graph:
distance travelled = time interval ∙ velocity
2) Constantly accelerated motion
Sometimes an accelerating object will change its velocity by the same amount each second. E.g. an
object changes its velocity by 10 m/s in each consecutive second. This is referred to as a constant
acceleration since the velocity is changing by a constant amount each second. An object with a
constant acceleration should not be confused with an object with a constant velocity.
Distance – time graph
Velocity – time graph
Acceleration – time graph
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PREMEDICAL COURSE – PHYSICS
2. KINETICS
FREE FALL
One of the most famous stories about free fall joins to Galileo. He one dropped two metal balls off
the Leaning Tower of Pisa. He proved that heavier objects do not fall faster than lighter ones.
A free falling object is an object that is falling under the sole influence of gravity. Any object that is
being acted upon only by the force of gravity is said to be in a state of free fall. This value (known as
the acceleration of gravity) is the same for all free-falling objects regardless of how long they have
been falling, or whether they were initially dropped from rest or thrown up into the air.
More massive objects will only fall faster if there is an appreciable amount of air resistance present.
The Free Fall is constantly accelerated motion.
There are two important motion characteristics that are true of free-falling objects:
Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s2.
Symbols and units:
distance →d or s (the Latin word ’spatium’ means space) [m]
displacement → or [m]
speed → v [miles/hour, m/s, km/h]
velocity → [miles/hour, m/s, km/h]
acceleration → a [m/s2]
gravitational acceleration → g [m/s2] = 9.81 m/s2
ADDITIONAL QUESTIONS
1) A car is moving at first with a speed of 25 km/h for 4 minutes then 50 km/h for another 8
minutes. Finally it is moving 20 km/h which takes 2 minutes. Calculate the total travelled
distance, in km and the average speed in SI units!
Answers: 9 km; 10.7 m/s
2) The airplane accelerates until 12 s before the take off (d=600 m).
a) Determine the acceleration.
b) Calculate the velocity at the end of 12th s.
c) Determine the travelled distance in the last 1 s.
Answers: 8,33 m/s2; 100 m/s; 96 m
3) How long does a body fall down from 10 cm, and how much is its velocity at the moment of
the touch-down? (g=10 m/s2)
Answer: 0.14 s; 1.4 m/s
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PREMEDICAL COURSE – PHYSICS
2. KINETICS
4) A train is moving at first with a constant velocity (v = 36 km/h). After 15 min the train begins
to accelerate and after 5 min it achieves 72 km/h and it does not accelerate any further.
a) How great the acceleration is (m/s2)?
After 5 min it starts to decelerate with 2 m/s2.
b) How long distance and how many seconds does the train need to stop?
c) How long is the total travelled distance? Calculate the average speed?
http://www.regentsprep.org/Regents/physics/phys01/velocity/default.htm
http://www.physicsclassroom.com
http://www.physicstutorials.org/home/mechanics/1d-kinematics/free-fall
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