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Equations of Motion - The Physics Hypertextbook
physics.info/
This is the way things get done in physics. It is such a useful
technique that we will use it over and over again. Our goal in this
section, is to derive new equations .. |
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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. The variety of
representations that we have investigated includes
verbal representations, pictorial representations,
numerical representations, and graphical representations
(position-time graphs and velocity-time graphs). In
Lesson 6, we will investigate the use of equations to
describe and represent the motion of objects. These
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 the car is fully
described. And if a second car is known to accelerate
from a rest position with an eastward acceleration of
3.0 m/s2 for a time of 8.0 seconds, providing a final
velocity of 24 m/s, East and an eastward displacement of
96 meters, then the motion of this car is fully
described. These two statements provide a complete
description of the motion of an 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, while the rest are unknown. For example as you
approach the 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 that 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 stop. In such
an instance as this, the unknown parameters can be
determined using physics principles and mathematical
equations (the kinematic equations).
The kinematic equations are a set of four equations that
can be utilized to predict unknown information about an
object's motion if other information is known. The
equations can be utilized for any motion that can be
described as being either a constant velocity motion (an
acceleration of 0 m/s/s) or a constant acceleration
motion. They can never be used over any time period
during which the acceleration is changing. Each of the
kinematic equations include four variables. If the
values of three of the four 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 information is known. For example, if the
acceleration value and the initial and final velocity
values of a skidding car is known, then the displacement
of the car and the time can be predicted using the
kinematic equations. Lesson 6 of this unit will focus
upon the use of the kinematic equations to predict the
numerical values of unknown quantities for an object's
motion.
The four kinematic equations that describe an object's
motion are:
There are a variety of symbols used in the above
equations. Each symbol has its own specific meaning. The
symbol d stands for the displacement of the object. The
symbol t stands for the time for which the object moved.
The symbol a stands for the acceleration of the object.
And the symbol v stands for the velocity of the object;
a subscript of i after the v (as in vi) indicates that
the velocity value is the initial velocity value and a
subscript of f (as in vf) indicates that the velocity
value is the final velocity value.
Each of these four equations appropriately describes the
mathematical relationship between the parameters of an
object's motion. As such, they can be used to predict
unknown information about an object's motion if other
information is known. In the next part of Lesson 6 we
will investigate the process of doing this.
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