Lesson 6: Describing Motion with Equations
The Kinematic
Equations
The goal of this first unit of The Physics Classroom has
been to investigate the variety of means by which the motion
of objects can be described. These representations
include verbal
representations, pictorial
representations, numerical representations, and
graphical representations (position-time
graphs and velocity-time
graphs). Lesson 6 investigates the use of
equations to describe and represent the motion of objects.
Such equations are known as
kinematic
equations.
There are a
variety of quantities associated with the motion of objects
– displacement (and distance),
velocity (and speed), acceleration,
and time. Knowledge of each of these quantities provides
descriptive information about an object's motion. For
example, if a car is known to move with a constant velocity
of 22.0 m/s, North for 12.0 seconds for a northward
displacement of 264 meters, then the motion of that car is
fully described. If a second car is known to accelerate
from a rest position with an eastward acceleration of 3.0
m/s2 for 8.0 seconds, having a final
velocity of 24 m/s, East and an eastward displacement of 96
meters, then the motion of this car is also fully described.
Each of these two statements provides a complete description of the
motion of the object. However, such completeness is not
always known. It is often the case that only a few
parameters of an object's motion are known. For example
as you approach a stoplight, you
might know that your car has a velocity of 22 m/s, East and
is capable of a skidding acceleration of 8.0
m/s2, West. However, you do not know the
displacement your car would experience if you were to
slam on your brakes and skid to a stop; and you do not know
the time required to skid to a complete stop. In an instance such as
this, the unknown parameters must be determined using
physics principles and mathematical equations – the kinematic
equations.
Using the Kinematic Equations
The kinematic equations are a set of four
equations which can be utilized to determine unknown
information about an object's motion if other details are
known. The equations can be used for any motion described
as being either a constant velocity motion
(acceleration = 0 m/s/s) or a constant acceleration
motion. They can never be used for any time period during
which the acceleration is changing.
Each of the kinematic
equations includes four variables; if the values of three
variables are known, then the value of the fourth
variable can be calculated. In this manner, the kinematic
equations provide a useful means of predicting information
about an object's motion if other parameters of the motion are known. For
example, if the initial and final velocity of a skidding car
are known, then the displacement of the car and the time taken can
be predicted using the equations. Lesson 6 of this
unit will focus on the use of the kinematic equations to
predict the numerical values of the unknown quantities of an
object's motion.
The four kinematic equations which
describe an object's motion are:
![equations]()
There are a variety
of symbols used in the above equations and each symbol has a
specific meaning.
d – the
displacement
of the object.
t – the
time
for which the object moved.
a –
the acceleration
of the object.
vi – the initial velocity of the object.
vf – the final velocity of the object.
Each of the four equations appropriately
describes the mathematical relationship between the
parameters of an object's motion. The next
section of Lesson 6 investigates the process of
using these kinematic equations to determine unknown information
about an object's motion from the parameters that are known.
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