Machines Theory

Understanding kinematics

Kinematics is very useful in the conceptual design of mechanical systems. The model takes into account the initial body velocities and geometries. Kinematics can assist in assessing a design’s theoretical viability, but designing for the real world involves additional complexity. Many theoretically conceivable designs would be likely to fail without consideration of the materials and the forces operating upon them. In contrast to kinematics, kinetics takes into account physical properties like the mass of the bodies or the forces moving them.

Kinematics

Kinematics is analytically derived from kinematics by calculating physical properties and forces using algebra. Kinetics considers physical forces as well as material characteristics such as mass, stiffness, and tensile or compressive strength. These features can be used to take a theoretical model from kinematics and use physics and thermodynamics to determine how to construct a workable, dependable, and functional real-world system.

Today you will be learning the definition, types, examples, and equations of kinematics. You’ll also be learning the speed and velocity in kinematics with calculations.

What is kinematics?

Kinematics is the study of mechanical points, bodies, and systems in motion without taking into account the forces acting on them or their related physical properties. The study, often known as the geometry of motion, uses algebra to mathematically model these motions. Kinematic systems are modeled to calculate things like speeds and ratios. The gears of a car’s transmission serve as an illustration of a system’s bodies.

These models are used to design various kinds of mechanical devices and to simulate the motions of real physical objects, such as the motion-rigid, body-hinged mechanics of the human skeleton or the stellar kinematics, or motion of celestial bodies in astronomy. Kinematics is where a formal study of physics begins. The word “kinematics” is connected to other English words like “cinema” (movies) and “kinesiology” and derives from the Greek word “kinesis,” which means motion (the study of human motion).

Measurement of the kinematic parameters used to describe motion is known as kinematic analysis. Kinematics can be studied abstractly and converted to purely mathematical equations that can be used to calculate a variety of motion-related quantities, including velocity, acceleration, displacement, time, and trajectory.

Types of kinematics

Below are the common types of kinematics:

Speed
Velocity
Acceleration
Uniform motion

Speed

An object’s speed is determined by how fast it moves (the same as the ordinary, everyday definition). In physics, speed is described as the rate of change in position, irrespective of direction.

The basic formula for average speed is:

Average speed

Where,

Kinematicsstands for average speed.
stands for distance.
stands for time.

 

Velocity

Velocity is the rate at which a body’s position changes in a certain direction. The speed at which an object is moving in a specific direction, like a vehicle, is known as its velocity. A speed and a direction have to be given in order to specify the velocity. Using the vehicle from the previous example, if it is traveling east of west, its velocity will be 50 km/h, e of w.

Acceleration

The rate at which velocity changes is called acceleration. Considering the definition of velocity, this could indicate a shift in direction or speed. Therefore, even though the vehicle is moving at a constant speed of 50 km/h, if it turns around a curve without slowing down and continues on its way toward the south (for example), it is accelerating. When it comes to dynamics, the study of the forces that cause objects to move, acceleration will prove to be a relevant topic.

Read more: Understanding acceleration

Uniform motion

When the distance traveled changes by the same amount every second or when the speed is constant, the motion is the simplest type. We refer to this as uniform motion, and the following is a graph of the distance vs time:

Uniform motion

Keep in mind that the graph’s slope (rise/run) corresponds to the speed. The speed is constant, and the graph always has the same slope (steepness = rise and run). The deltas (change in) may be omitted and the formula v = d/t utilized when the distance at time zero is zero. This is frequently expressed as d = vt. Speed, which is the magnitude (size) of velocity, is frequently represented by the letter v.

Examples of kinematics

Below are few examples of kinematics.

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  • A person skydiving.
  • An orange that falls from a tree.
  • A car moving in a straight line.
  • Firing a cannonball.
  • A car accelerating from zero.
  • When a freekick is played in soccer game.
  • A ball being throw in baseball.
  • Shooting a basketball.

Read more: Understanding Machine

kinematics equations

The following are the four basic kinematics equations

Kinematics equations

Speed and velocity in kinematics

Speed

Speed is basically the rate at which a certain distance is covered. In terms of physics, we would say it is the rate at which distance is changing. Speed is a scalar quantity with simply a magnitude and no direction because it depends on distance, a scalar quantity. As a result, it will always be positive, similar to how speedometers on cars can only display positive numbers. The speed symbol (ss) in equations stands for the distance traveled divided by the time interval.

Formula for Speed
S = d/Δt

The time change here, denoted by the symbol tt, is measured in seconds (represented by an ss). The equation itself gives the units for speed. The units for speed are, rather logically, meters per second (represented by textm/sm/s), and the equation shows meters divided by seconds.

Velocity

The definition of velocity is somehow similar, but it refers to the rate of change of displacement rather than the rate of change of distance. No matter how long the trip was, velocity determines how quickly an object changes its position. Velocity is a vector quantity with a magnitude and a direction because it is based on displacement, a vector quantity. The symbol for velocity in equations is vv, and it is equal to displacement divided by time change.

Formula for Velocity
V = Δx/Δt

Furthermore, Δt is refers to the change in time. The equation can also be used to derive velocity units. Because distance is measured in meters and time is measured in seconds, we may calculate meters per second by dividing meters by seconds (still written as textm/sm/s). Take note: You may only see tt to indicate time rather than Delta tt depending on the level of physics course you are taking and the textbook your course is using.

Read more: Understanding Speed and velocity

Calculations of speed and velocity in kinematics

The following are few examples of speed and velocity in kinematics alongside with the answers:

Example 1

The speed and velocity of a round object

Now let’s look at a round object rolling down a hill. The hill is 50 m, and it takes 25 s for the object to finish rolling down the hill. So, find the speed and the velocity of the round object.

Answers

How to find the speed of the round object

For us to get the speed, we’ll start by laying out all the values we need.

Distance = 50 meters
Time        = 25 seconds

Now that we’ve laid out the values needed, we will then apply it to the formula we’re going to use, which is s = d/Δt.

s = d/Δt

s = 50 m/25 s

s = 2 m/s

And our final answer for the speed of the round object is 2 m/s.

How to find the velocity of the round object

We’re going to be solving for velocity the same way we solve for speed. But this time around, we will be laying out displacement and time instead of distance and time.

Displacement (Δx)  = −50 meters
Time (Δt)                   = 25 second

Now that we’ve laid out displacement and time, we should continue by applying it to the equation v = Δx/Δt

v = Δx/Δt

v = −50 m/25 s

v = −2 m/s

And our final answer for the velocity of the round object is −2 m/s.

Read more: Understanding distance and displacement

Example 2

Speed and velocity in going to school

Consider that your home, school, and favorite bakery are arranged as in the illustration above. Calculate your distance for the trip if you plan to stop at the bakery on your way to school in the morning to get a breakfast pastry.

Answers

How to Find the Distance in Going to School

For you to find the distance, you will need to account for the length of the entire trip – from the home, past the school, to the bakery, and then back to the school. Here is the mathematical representation:

distance = 60 m+30 m+30
distance = 120 m

And the total distance traveled from the home, past the school, to the bakery, and then back to the school is 120 meters.

Now let’s go back to the trip to school with a stop at the bakery. We already know this trip had a distance of 120 m and a displacement of 60 m. Let’s also assume the trip took 600 seconds(10 minutes). Find our speed and velocity.

How to Find Speed in Going to School

For us to get the speed, we’ll start by laying out all the values we need.

Distance (d) = 120 m
Time (Δt)      = 600 s

Now that we’ve laid out the values needed, we will then apply it to the equation we’re going to use, which is s = d/Δt.

s = d/Δt

s = 120 m/600 s

s = 0.2 m/s

How to Find Velocity in Going to School

We’re going to be solving for velocity the same way we solve for speed. But this time around, we will be laying out displacement and time instead of distance and time.

Displacement (Δx) = 60 m
Time (Δt)                  = 600 s

Now that we’ve laid out displacement and time, we should continue by applying it to the equation v = Δx/Δt

v = Δx/Δt

v = 60 m/600 s

v = 0.1 m/s

And our final answer for the velocity of going to school is 0.1 m/s.

Frequently Asked Questions (FAQs)

What is kinematics in physics?

The study of motion in a system of bodies is called kinematics, which does not directly take into account the forces or potential fields influencing the motion. In other words, kinematics examines the distribution of momentum and energy among interacting bodies.

What is kinematics in simple words?

Kinematics is the study of mechanical points, bodies, and systems in motion without taking into account the forces acting on them or their related physical properties. The study, often known as the geometry of motion, uses algebra to mathematically model these motions. Kinematic systems are modeled to calculate things like speeds and ratios.

What are the four kinematic equations?

Kinematics equations

What are examples of kinematics?

Below are few examples of kinematics:

  • A car moving in a straight line.
  • Firing a cannonball.
  • A car accelerating from zero.
  • When a freekick is played in soccer game.
  • A ball being throw in baseball.
  • Shooting a basketball.

How is kinematics used in everyday life?

For instance, kinematics can assist you in figuring out the acceleration and velocity of the moving object at each point in time if you were to construct a system that could transport an object from one location to another automatically.

What is the difference between kinetics and kinematics?

Kinetics is concerned with figuring out what causes various motions of an object, like rotational motion, in which the object encounters force or torque. Acceleration, velocity, and object position are all explained by kinematics.

What is kinematic and dynamic?

Dynamics is the study of motions that are the result of forces, whereas kinematics is the study of motions without respect to the forces that cause them. The terms multibody dynamics, mechanical system simulation, and even virtual prototyping are also used to describe the same kinds of studies.

What is the kinetic energy formula?

K.E. = 1/2 m v2.

Who invented kinematics?

The German engineering scientist Franz Reuleaux (1829–1905), commonly referred to as the “father of kinematics,” made significant contributions to the study of kinematics and the theory of machines in the late 19th century, which are addressed in this review.

Can velocity be negative?

A change in position (displacement) over a period of time is referred to as an object’s velocity. Speed can only be positive, whereas velocity can be either positive or negative because it involves both speed and direction.

Is speed and velocity the same?

Velocity is the speed and direction of an object’s movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity.

Are kinematics easy?

One of the simplest and most significant chapters of mechanics included in the IIT JEE, AIEEE, and other engineering examinations’ syllabus is kinematics. In addition, beginners find it easy and quite exciting to answer numerical problems.

That is all for this article, where the definition, types, examples, equations, and speed and velocity in kinematics with calculations have been discussed.

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