# What is Kinematics: Definition and 999 Discussions

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.
Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. They are also central to dynamic analysis.
Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.

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1. ### A ball is thrown w/initial speed vi at an angle 𝜃i with the horizontal

A ball is thrown with an initial speed vi at an angle 𝜃i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/8. In terms of R and g, find the following. (a) the time interval during which the ball is in motion: Sroot(R/g) Correct (b) the ball's...
2. ### 'Police Car Catching Up' problem in kinematics

Why is it 10.92 seconds and not 10 Cars displacement = 30*t +1/2(0)t^2 police displacement = 0*t + 1/2(6)(t)^2 30t = 3t^2 t = 10 seconds ???
3. ### B The Beacons Problem

I propose to you a kinematics problem described by classical physics. Three space beacons A, B and C are 300,000,000 m (approximately one light second) apart. Beacon A emits a bright flash every three seconds. Beacons B and C respond instantly to the flash of Beacon A by emitting...

idk
5. ### Projectile motion, initial height and range given, find initial velocity

the answer to this question uses the above formula with the tangent function and solves for the initial velocity, i used the equation (v.sinθ^2) = (v.sinθ)^2 - 2gΔy, setting final velocity equal to zero and solving for initial velocity. this kinematic equation gives a different answer. can...
6. ### B Kinematic equations ##\textbf{purely}## from graphs

1. The first equation between velocity ##v## and time ##t## can be derived using the graph I have drawn for the purpose as shown on the right. Since acceleration ##a_0## is a constant, the graph of ##v-t## is a straight line. The slope of the line is ##\dfrac{v-v_0}{t} = a_0\Rightarrow \boxed{v...
7. ### Calculating the Average speed given two speeds

$$v_1= 115km/h$$ $$v_2= 60km/h$$ solution: $$\frac {v_1 + v_2}{2}$$
8. ### Kinematics: 100 meter dash when one runner starts 3 seconds later

$$t_A= 3s$$ $$s= 100m$$ $$v_A= 5m/s$$ $$v_B=7m/s$$ $$s(t)=7(t-3)+0$$
9. ### B Rotational Kinematics -- questions about a=mg sin(theta) / (m+I/R^2)

Hi, I am learning. Rotational Kinematics and I was given this formula in class: a=mgsin(theta)/(m+I/R^2); however, I couldn't understand the professor's explanation of where it comes from. Could someone provide some insights about it? I appreciate any help you can provide.
10. ### Frames of Reference: Find the speed and heading of the airplane

so far what i have gotten to is that 300/0.75 = 400km/h but I dont know how to draw the diagram for this
11. ### I Relativity of simultaneity

When two remote events are observed/measured to be simultaneous in one inertial frame, the same events will not be simultaneous when observed from a second frame in uniform motion relative to the first. Why is this distinction in the kinematics of light not considered an operational distinction...
12. ### 8.01 MIT OCW PS1.4: Throw and Catch (Kinematics)

1) Using "The person catches the ball at exactly the same height it was thrown from.", we can isolate t by solving yb(t) = v0*sin(theta)*t - (1/2)*g*(t^2) = 0: yb(t) = v0*sin(theta)*t - (1/2)*g*(t^2) = 0 v0*sin(theta)*t = (1/2)*g*(t^2) 2*v0*sin(theta) = g*t t = 2*v0*sin(theta) / g 2) At the...
13. ### Jaan Kalda Kinematics question -- What regions can this cannon reach with its projectile?

what i tried to do is to write y=v_0tsin alpha - 1/2gt^2 and x=v_0 cos alpha tand that t=x/v_0 cos alphai plug t in the formula for y and get that y= x tan alpha - gx^2/v_0^2 (tan^2 alpha -1)since jaan klada said there should be a quadratic equation (because its a parabola) i thought that...
14. ### Velocity vs Speed (What's more relevant here?)

This is a famous book in India. I was wondering if one could say if the answer should include velocity or speed. I mean, I don't think there are any details which hint at velocity. We are gives speed in the question and we are asked to find out the distance traveled, this hints we are asked to...
15. ### [Kinematics] Calculating the maximum height reached by the ball

I realize I can solve the other way too. But I want to solve using the equations ##v = u +at## ##S = ut +0.5(at^2)## and I don't know why I didn't get the right answer. Thank you for your help!
16. ### I Drawback of dimensional analysis - motion in a resistive medium

Statement from the text : I copy and paste the portion of the text that am struggling to understand and underline in red the claim the author makes which I can't believe to be true. Doubt : As you can read in the first line of the paragraph and in the one I underlined, the author believes that...

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18. ### Calculus Problem: Blowing Up a Spherical Balloon

I'm struggling with section a. This is my calculation: The expression remains depend on the variable t, while in the answer is a concrete number:
19. ### Chain rule and division by zero

My approach is as follows: a = dv/dt = (dv/dx) * (dx/dt) = (dv/dx) * v Putting v = 0: a = (dv/dx) * 0 = 0 m s^(-2) But, what I don't understand is this: If v=0, then dx/dt must also be 0. Consequently, dx must also be 0 at that particular instant. But, we are writing acceleration as (dv/dx) *...
20. ### I know everything to do on this problem except one thing

Even though I have all the formulas needed to do this problem, I cant figure out how to get rA, rB and rA' aswell as rB'
21. ### 2D kinematics problem -- Skateboard ramp jump calculations

So I tried the following: Getting the velocities for x and y V_xi = 5.2cos(30) = 4.5 V_yi = 5.2sin(30) = 2.6 Then I use v^2 = u^2 +2as to get the final velocities before she leaves the ramp: for V_x the final is the same as the initial since the equation becomes V_xf = V_xi for V_y the final is...
22. ### Rock falling down a tunnel

all i could accomplish was calculating the distance between P and the ceiling in a horizontal line(6)
23. ### Kinematics : Average velocity problem

The car covers half of the road with an average velocity of v, so the elapsed time is equal to: ##t_1=\frac {d/2} {v}=\frac {d} {2v}## And it covers 1/4 of the road with an average velocity of 2v, so the elapsed time is equal to: ##t_2=\frac {d/4} {2v}=\frac {d} {8v}## Then it covers 1/8 of the...
24. ### Mechanics for High School Students: Building a Robotic Arm

TL;DR Summary: Mechanical engineering,robotics,mechnics,dynamics Hi guys , I'm new to mechnics and I want to learn it for building robotic arm , but I find mechanics book topics somewhat difficult for me , what I need to learn to get started as I'm a highschool student with basic level math.
25. ### Flag orientation for a boat observer Vs a ground observer

I am confused by the question. So, the first thing I am trying to understand is whether the flag direction will be same to a boat observer as to a ground observer. I know that the flag will orient itself in the direction the wind is blowing towards, so the flag should always point in NE...
26. ### Find the value of ##t## when ##P## returns to ##X##- Kinematics

My interest is on part (e) only parts a - d were quite easy. I seek an alternative approach for part (e) ...phew this was a nice one ...took me time to figure out. :cool: Find the text solution here: My take/approach; We have ##a=0.6 m/s^2##, therefore; using ##s=ut+\dfrac{1}{2}at^2##, we...
27. ### Towards a new theory of information kinematics

The physical world is highly parallel; many things are happening side by side simultaneously. This is true not only at the macroscopic scales that we can see but as far as we know down to the subatomic scales. This is referred to as the principle of locality [1], which states that an object is...

29. ### Projectile motion problem – determining initial velocity of throw

My reasoning was to use this kinematic equation to first get time of flight of the baseball using horizontal components, and then use this same equation again to find initial velocity.
30. ### Kinematics of movement subject to a variable acceleration

Can someone guide me how can I find time ?! I don't have any idea. This is a part of a question in Classical Dynamics.
31. ### I Deviations of conservation laws in cosmological evolution?

If energy is "not conserved" in General Relativity (or at least, it is difficult to define it) in the context of an expanding accelerating spacetime (like it happens in our Universe), are there any observations of deviations from the strict conservation laws in the evolution and formation of...
32. ### Force and Kinematics -- Accelerating a 10kg box vertically

I realize that there is a downward force of gravity weighing the object toward earth’s surface, equaling F = mg (downward). The upward force would have to be something at least as much as the downward force in order to lift the object up ”such that it is accelerated from rest to a velocity of 5...
33. ### Incorrect Textbook Answer involving kinematics?

vf=0 km/hr vi = 100 km/hr x = 80,000 km vf2 = vi2+2ax 0 = 100^2 + 2a(80,000) 160,000a = -10000 a = -0.0625 km/hr^2 This is off by 1,000,000 times from the textbook answer. Am I missing something with units or something or is the book wrong?
34. ### Relative velocity Question for a Ferryboat

So far I have this: vbwx= 4.40c0s(28) = 3.88496409 vbwy= 4.40sin28 = 2.065674876 vpwx= 4.4ocos28 vpwy= 4.40sin28 +2.02 Find Square root of vpx^2 + vpy^2 = 5.43? Im confused as to whether we add the 2.02 to the sin28 or the cos28 though, did I do it right? Also, not sure how to find the...
35. ### Questioning the Solution for Elevator vs Rock Problem

Hi everyone I have solutions to this problem, but I am not sure if the premise behind them is correct. I think this is the reasoning behind the solution for question d. - Work out how far the elevator travels in the 7s before the rock is thrown, so 7x2.5 = 17.5 - Work out how far the...
36. ### A Relativistic Relative Velocity Comp.: Bini, D. et al. (1995)

I'm trying to understand this paper (equation 2.16 specifically): Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition...
37. ### Apparent weight problem (kinematics + conservation of Energy + Newton's laws)

Hello there, I have tried the problem but don't get a different of 6g's as I am supposed to. I am not sure whether I interpreted the problem in the correct way, but I would love some feedback/hints on what went wrong in my solution, thanks in advance. Solution: SITUATION DRAWINGS + FBDS so...
38. ### I Deriving kinematic equation for position

We usually have an initial time and then find an equation for the variable final time. Can we derive a formula to calculate position with final time and variable initial time. ##v = v_i + a(t_f - t_i)## ##dx = v_idt + at_fdt - atdt## integrating ##x_f - x_i = v_i(t_f - t_i) + at_f(t_f - t) -...
39. ### Three Points at Vertices of Equilateral Triangle

I’m not sure of how to begin solving this problem. I attempted to draw a diagram and finding the components velocity of each initial velocity vector but this did not lead anywhere. Could so please have a hint?
40. ### I Momentum, impact force and Earth

Suppose two objects, A and B, with large lengths LA and LB, and masses MA and MB, collide at time t0. Both objects before collision are vertical and aligned concentrically, being object B positioned initially at a higher z coordinate than object A. The bottom end of object A is rigidly...
41. ### I Forward kinematics of a snake robot

i want to build a forward kinematic model of a snake robot, to find its end-effector position am already worked on a few robotic arms like puma 560 using the DH table so i tried using the DH table on the snake robot, but it seemed wrong, so how do i do it ? the snake robot is similar to the...
42. ### Ball rolling down a slope problem: Find an expression for time taken

Question: Galileo released a metal ball from rest so that it could roll down a smooth inclined plane. The time t taken to roll a distance s was measured. He repeated the experiment, each time recording the time taken to travel a different fraction of the distance s. Write an expression for the...
43. ### Relating Linear and Angular Kinematics

a) We use the definition of linear speed in terms of angular speed: v = r*omega omega_f = v/r = (1.25 m/s)/(0.025 m) = 50 rad/s omega_0 = v/r = (1.25 m/s)/(0.025 m) = 21.55 rad/s b) We use the definition of linear speed: v = d/t d = vt = (1.25m/s)(74 min)(60 s/1 min) = 5.55 km c) We use the...
44. ### Kinematics - can't find the initial velocity according to the image

I tried to write the data I understood from the image: y0=160m yf=0 x0=0 x1=192m I tried to express the total change in time using the position over time equation on the Y direction: y(t)=y0+v0y*(t2-t1)-0.5a(t2-t1)^2 but then I stuck with 2 variables and didn't know what to do any help?
45. ### B Misleading Textbook Equation for vf^2=vi^2 + 2ad

The textbook (Nelson 11) at my school lists the "big 5" equations for uniform acceleration. In all but one, they use vectors. For vf^2=vi^2 + 2ad, the opt not to use vectors. Is there a deep reason why we would not want to use the vectors? I understand that when you square the velocity, the...
46. ### 100m dash kinematics problem

So what I have done is that on question 7 I know he is accelerating to constant my knowns are that it is from initial and acceleration is given so I have that for my first phase the second phase is that Your vfinal is your new initial for it and acceleration is the constant but you don't know...
47. ### 2D kinematics -- Calculate the acceleration of the jumping athlete

this is my work but the answers say 11 m/s^2 so I made an error somewhere. Also if someone could help me with solving the direction for the acceleration, that would be greatly appreciated.
48. ### Simple kinematics question -- Riding a bicycle race in two different gears

I calculated average velocity but obviously it helps nothing with this problem. I hope to get me going with these exercises once I break the ice. Thank you in advance!
49. ### Halliday Resnick Krane Chapter 2 Problem 30: Juggling Five Balls

If each ball rises two meters, then the time is in the air is equal to around 1.28 seconds. After this, what am I supposed to do? I feel really stuck. If all of the balls are released at different times, how am I supposed to find the answer?
50. ### Roundtrip by Plane: Understanding Wind & Velocity Effects

The question I have is that if the aero plane is traveling in the same direction as the wind, would it not increase its velocity, as in with boats and streams? So, if by chance, ##w = v##, then the velocity of the aero plane would double. It feels weird as going by the same logic, if the speed...