What Are Kinematic Formulas and How Do They Work?

Equations of Kinematics: The purpose of this first lesson of The Physics Classroom was to study the various methods for describing the motion of objects. Verbal representations, pictorial representations, numerical representations, and graphical representations are among the many types of representations we’ve looked into (position-time graphs and velocity-time graphs).

In Lesson 6, we’ll look at how to utilize equations to describe and express object motion. Kinematic equations are the name for these equations. The motion of things is described by several quantities: displacement (and distance), velocity (and speed), acceleration, and time.

 

What Are Kinematic Formulas and How Do They Work?

 

Each of these numbers provides descriptive information on the motion of an object. For example, if a car moves at a constant speed of 22.0 m/s north for 12.0 seconds, resulting in a 264-meter northward displacement, the motion of the car is fully described. And if a second car is known to accelerate from a stop at 3.0 m/s2 eastward for 8.0 seconds, resulting in 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 assertions provide a comprehensive account of an object’s motion. This completeness, however, is not always known. Only a few parameters of an object’s motion are frequently known, while the rest are uncertain. As you approach the stoplight, for example, you may be aware that your automobile has a speed of 22 m/s east and a skidding acceleration of 8.0 m/s2 west.

 

However, you have no idea how much displacement your automobile would feel if you slam on the brakes and skid to a stop; and you have no idea how long it would take to skid to a stop. The unknown parameters in this case can be determined utilizing physics principles and mathematical equations (the kinematic equations)

 

There are four kinematic equations in total.

 

Kinematics is the study of moving objects and their interactions. There are four (4) kinematic equations that relate to displacement, velocity, time, and acceleration, and they are D, v, t, and a.

 

(vi +vf)/2 = D/t a) D = vit + 1/2 at2 b) (vi +vf)/2 = D/t

 

vf2 = vi2 + 2aD c) a = (vf – vi)/t d) vf2 = vi2 + 2aD

 

D stands for displacement.

 

a = rate of change

 

t stands for time.

 

final velocity (vf)

 

beginning velocity vi

 

What do the three kinematic equations mean?

 

If we know three of these five kinematic variables for an object under continuous acceleration— x, t, v 0, v, a Delta x, t, v 0, v, an x,t,v0,v,adelta, x, comma, t, comma, v, start subscript, 0, end subscript, comma, v, comma, an x

 

What is the total number of kinematic equations?

 

There are four kinematic equations in total.

 

The four kinematic equations that describe the motion of an object are as follows: In the equations above, a number of symbols are employed. Each sign has a distinct meaning. The object’s displacement is represented by the symbol d.

 

What is the purpose of kinematic equations?

 

Different aspects of motion, such as velocity, acceleration, displacement, and time, can be calculated using kinematic equations.

 

List of Kinematic Equations

 

The kinematic formulas are a collection of equations that relate to the five kinematic variables listed below.

 

a large one

 

quad v=v0+at1 quad v=v0+at1 quad v=v0+

 

v=v0+at1,

 

start subscript, 0, end subscript, plus, a, t, point, space, v, equals, v, start subscript, 0, end subscript, plus, a, t

 

2 x Large

 

quad Delta x=(dfracv+v 02) quad Delta x=(dfracv+v 02) quad Delta x=(dfracv+v 02) quad Delta x=(dfracv+v 02) quad

 

t2

 

Δx=(2v+v0)t2,

 

start fraction, v, plus, v, start subscript, 0, end subscript, divided by, 2, end fraction, right parenthesis, t, point, space, delta, x, equals, left parenthesis, start fraction, v, plus, v, start subscript, 0, end subscript, divided by, 2, end fraction, right parenthesis, t

 

  1. Extra-large

 

quadDelta x=v 0 t+dfrac12at23 quadDelta x=v 0

 

Δx=v0t+21at23,

 

point, space, delta, x, equals, v, start subscript, 0, end subscript, t, plus, start fraction, 1, divided by, 2, end fraction, a, t, start superscript, 2, end superscript, a, t, start superscript, 2, end superscript, a, t, start superscript, 2, end superscript, a, t, start superscript, 2, end superscript, a, t, start superscript, 2, end super

 

4 x Large

 

quad v2=v 02+2aDelta x4 quad v2=v 02+2aDelta x4

 

v2=v02+2aΔx4,

 

a point, a space v, start superscript, 2, end superscript, equals, v, start subscript, 0, end subscript, start superscript, 2, end superscript, plus, 2, a, delta, x, v, start subscript, 0, end subscript, start superscript, 2, end superscript, plus, 2, a, delta, x

 

We must be careful not to apply the kinematic formulas when the acceleration is changing because they are only accurate if the acceleration is constant over the time frame considered. The kinematic formulas also require that all variables correspond to the same direction: horizontal xxx, vertical yyy, and so on.

 

Also see How To Work Out The Angular Velocity Formula.

 

Equations of Angular Kinematics

 

Any item that accelerates solely due to gravity is referred to as a freely flying object. We usually assume that the effect of air resistance is small enough to ignore, which means that any object dropped, thrown, or otherwise flying freely through the air is assumed to be a freely flying projectile with a constant downward acceleration of magnitude g=9.81dfractextmtexts2g=9.81s2mg, equal, 9, point, 81, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction.

 

When we consider it, this is both unusual and fortunate. This is peculiar since it indicates that a massive rock will speed downwards at the same pace as a small pebble, and that if they were dropped from the same height, they would hit the earth at the same moment.

 

[How is this possible?]

 

It’s fortunate, because while solving kinematic formulas, we don’t need to know the mass of the projectile because the freely flying item will have the same amount of acceleration, g=9.81dfractextmtexts2.

 

g=9.81s2mg, equals, 9, point, 81, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction, regardless of mass

 

Note that g=9.81dfractextmtexts2g=9.81s2mg equals 9, point, 81, start fraction, m, divided by, s, start superscript, 2, stop superscript, end fraction. When we plug into the kinematic formulas for a projectile, we must make the acceleration due to gravity negative a y=-9.81dfractextmtexts2ay=9.81s2ma, start subscript, y, end subscript, equals, minus, 9, point, 81, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction

 

Also see: Average and Instantaneous Change Rates

 

Kinematic Equations in Physics

 

If other information about an object’s motion is known, the kinematic equations can be used to predict unknown information about its motion. The equations can be applied to any motion that is either a constant velocity motion (with an acceleration of 0 m/s/s) or a constant acceleration motion (with an acceleration of 0 m/s/s). They can’t be used during any time period where the acceleration is changing. There are four variables in each of the kinematic equations. The value of the fourth variable can be computed if the values of three of the four variables are known. In this way, the kinematic equations can be used to anticipate information about an object’s motion if other data is available.

 

For example, if the acceleration and initial and final velocity values of a sliding car are known, the kinematic equations can be used to forecast the car’s displacement and time. The use of kinematic equations to forecast the numerical values of unknown quantities for an object’s motion will be the subject of this unit’s sixth lesson.

 

The four kinematic equations that describe the motion of an object are as follows:

 

In the equations above, a number of symbols are employed. Each sign has a distinct meaning. The object’s displacement is represented by the symbol d. The symbol t represents the amount of time that the object travelled. The symbol represents the object’s acceleration. And the symbol v denotes the object’s velocity; a subscript of I following the v (as in vi) denotes the start velocity value, while a subscript of f (as in vf) denotes the final velocity value.

 

The mathematical relationship between the parameters of an object’s motion is accurately described by each of these four equations. As a result, if additional information about an object’s motion is known, they can be used to forecast unknown information about its motion. We’ll go into the process of doing this in the next section of Lesson 6.

 

Also see: Formula for Linear Interpolation

 

Equations of Kinematics (Basic Kinematics)

 

Kinematics is the study of object motion without regard for the forces that cause the motion. These well-known equations assist students to evaluate and predict object motion, and they will continue to utilize them throughout their physics studies. In order to succeed in physics, you must have a thorough understanding of these equations and how to use them to solve problems. This article is primarily a mathematical exercise intended to provide a fast refresher of how algebra is used to generate kinematics equations.

 

This activity is based on the diagram in Figure 1, where the x axis represents time and the y axis indicates velocity. The object’s motion is represented by the diagonal line, which changes velocity at a steady rate. The shaded region (A1 + A2) indicates the object’s displacement between t1 and t2, during which time the object’s velocity increased from v1 to v2.

 

The following variables will be used in this document:

 

v (meters per second, m/s) is the magnitude of the object’s velocity.

 

v1 (meters per second, m/s) is the magnitude of the initial velocity. (In some manuscripts, vi or v0 is used)

 

v2 = the final velocity magnitude (meters per second, m/s) (This is vf in certain manuscripts)

 

a = acceleration magnitude (in meters per second squared, m/s2)

 

The magnitude of the displacement is the distance, and s = the displacement vector

 

d = d = s = s = s = s = s = s = s = (vectors are indicated in bold; the same symbol not in bold represents the magnitude of the vector)

 

v = (v2 –v1), for example, denotes change.

 

t stands for time.

 

t1 is the start time.

 

t2 denotes the end time.