Kinematic Definition and 101 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. NODARman

    Number of collisions by a bullet

    How to find the collision number if the moving bullet hits a few wooden blocks and every collision takes 10 percent of its speed. In which block will the bullet stay?
  2. dorothy

    Several practice questions in Kinematics -- Average speed, projectile motion, distance covered

    The attached pdf is my solution. Thank you!
  3. Mjusttheletter

    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...
  4. runningphysics

    Vector Kinematics -- A particle leaves the origin with an intial velocity and experiences constant acceleration

    I'm not sure where to start, when I tired using integration of the initial equation to get pos(t)=-.65t^2 i + .13t^2 j + 14ti +13tj but after separating each component, i and j, and setting j equal to zero I got 0 or -100 seconds which doesn't seem like a reasonable answer.
  5. ayans2495

    Kinematics and One Dimensional Motion

    Would we assume that the deceleration of both instance are the same?
  6. mncyapntsi

    1-D Motion, calculating final velocity

    Hello! I have done this problem : vf^2 = (4.0x10^5)^2 + 2(6.0x10^12)(5x10^-3) so vf= sqrt((4.0x10^5)^2 + 2(6.0x10^12)(5x10^-3)) I get vf = 4.7 x 10^5 m/s However, the textbook solutions says vf = 8.7x10^5 m/s. Where did I go wrong? Thank you for any help! :)
  7. mncyapntsi

    Acceleration and speed -- confused

    I've written in that only the first statement was False, however my classmates aren't getting the same answer? Please help clarify...
  8. R

    Show that a projectile lands at a distance ##R = \frac{2v_0^2 sin \theta cos(\theta + \phi)}{g cos^2 \phi}##

    ##V_x = V_0 cos \theta ## ##x = V_0 cos \theta t## ##V_y = V_0 cos \theta ## ##y = V_0 cos \theta t## ##F_x = m\ddot{x}## ##-mgsin \phi = m\ddot{x}## ##\dot{x} = -gtsin\phi + V_x## ##x = -\frac{1}{2} gt^2 sin \phi + V_x t## ##x = -\frac{1}{2} gt^2 sin \phi + v_0 cos\theta t## ##F_y =...
  9. S

    Equations for a mass falling to Earth from a distance

    I have a question : If we consider the change in g due to distance from the earth core; then y=distance from earth’s core t=time G=gravitation constant M=Earth’s mass k=GM $$y^2(t)=\frac{k}{y(t)^2}$$ If we consider air resistive force as proportional to speed squared, then: m=falling object...
  10. wcjy

    Electric field problem using Gauss' law: Point charge moving near a line charge

    F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => Im not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so i...
  11. burian

    Application of momentum conservation in inelastic collisions

    So, what I did was suppose the mass of ramp is $ M_r$ and let velocity at B of block be v, then, after inellastic collsion both bodies v' velocity at B , $$M\vec{v}= M_r \vec{v'}+ M \vec{v'}$$ or, $$ \frac{M}{M +M_r} \vec{v}= \vec{v'}$$ Now, Suppose I take the limit as mass of ramp goes to...
  12. Tymofei

    Calculating the Moment from a Different Vantage Point

    Summary:: Just a simple 3d rigid dynamics question which im trying to solve by placing coordinat system differently from original solution.Everything looks ok but results are different. Mod note: Post moved from technical section. Thats my question.As you see coordinate system was located at...
  13. V

    Finding the y-component of a velocity vector

    The first thing I did, was to find the equations for player A (p) and ball's (b) path (for each i and j component I used the equation I wrote in the relevant equations) and then I found the derivative of both equations so I could have the velocity: $$\vec{r}_p(t)=(6t^2+3t)\hat{i}+20\hat{j}...
  14. IamVector

    Hard kinematics problem: Block pushed onto a moving conveyor belt

    stuck on this question
  15. E

    Maximum Distance a Projectile Moves Up an Inclined Plane

    the red line is the initial velocity, the grey parabola is the path of the projectile. hi there...I'm kinda stuck at the part b of this problem. I can do part a with no problem. can anybody explain to me how to do the differentiation needed to solve part b?? by explain I mean explain the...
  16. M

    Kinematics Problem: constant acceleration, motion in a line

    I've been attempting to solve this problem for three days now. I have thrown away my old attempts (like, scrumpled up into the bin), but my old attempts involved: Trying to set up simultaeneous equations relating the journeys between EH and FG to find the deceleration, but the reason why this...
  17. Like Tony Stark

    Doubts on the sign of acceleration

    What should I do? Because I have two possibilities. I have ##0=5+at## so ##-5/t =a##. But then I can also say that the acceleration is a negative because it is stopping, so I can write it like ##0=5-kt## and then ##5/t =k##
  18. J

    Kinematics of a kicked football

  19. Like Tony Stark

    Relative rotational motion on a disc

    The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot...
  20. Santilopez10

    Kinematics question on 2 planes moving relatively with each other

    So my problem isn't actually finding the components, but knowing if the initial approach I took is correct. So what I did was: At first I found that at the same instant, ##x_{B/A}=10500 m## so then I wrote the equation of motion for plane B respect to A: so $$\vec a_{B/O}- \vec a_{A/O}=\vec...
  21. Santilopez10

    Raising a bag with a rope

    So what I did was at first consider the case the kid is below the branch, so that x=0,t=0, then I thought that the lenght L of the rope should be ##L=2h## because we know the radius from the branch to the kid is just ##x^2+y^2=r^2## and when x=0, y=h. So then I wrote the motion equations for the...
  22. Santilopez10

    Intrinsic coordinates kinematics problem

    So I know that ##a_t = \frac{dv}{dt}=-ks## and ##\frac{dv}{dt}=v\frac{dv}{ds}## then: $$v dv=-ks ds \rightarrow (v(s))^2=-ks^2+c$$ and using my initial conditions it follows that: $$(3.6)^2=c \approx 13$$ and $$(1.8)^2=13-5.4k \rightarrow k=1.8 \rightarrow (v(s))^2=13-1.8s$$ What bothers me is...
  23. Santilopez10

    Plane being tracked by radar

    I tried to workout the problem but I find motion in different coordinates systems a bit weird at the moment, so only thing I could do is realise that the x component of ##\vec r(t)## is: $$vt +x_0$$ but for simplicity we will use the initial condition ##x_0=0## so that ##t_0## is the moment the...
  24. J

    Equation of motion of a mass on a 2d curve

    So ##T+U=\frac{1}{2}m(\dot{x}^{2}+\dot{y}^{2})-mgy=constant##. If I derive this with respect to ##t## $$\dot{x}\ddot{x}+\dot{y}\ddot{y}-g\dot{y}=0$$ Then I use ##\dot{y}=\dot{x}\frac{dy}{dx},\ddot{y}=\ddot{x}\frac{dy}{dx}+\dot{x}^{2}\frac{d^{2}y}{dx^{2}}## to get...
  25. E

    Airtime for halfpipe skateboarder

    I've calculated the potential energy at the top of the halfpipe, before the boarder drops in: PE = 39.5 kg * 9.8 m/s^2 * 3.66 m = 1416 J Since the boarder would have no potential energy and all kinetic energy at the bottom of the halfpipe, KE = 1/2mv^2 = 1416 J 1/2 (39.5 kg) (v^2) = 1416 J So...
  26. msfd

    Question regarding this Basketball Kinematics Diagram

  27. V

    Man on ladder: jump off instantly vs last moment?

    So there are two cases: a). free fall (straight forward for me) b). ladder rotating and jumping off in last moment (I am interested in trying to understand this case) I believe I should take into account momentum at the time the man hits the ground in both cases? The smaller, the better. Or...
  28. V

    Pitcher throwing a baseball

    Hello. I have just started studying physics. Can someone explain to me how can I type in formulas here using Tex for nicer formatting? I suppose the force is F = ma. Question is: what is a? The starting throw angle is not mentioned, I suppose this task has to be related to gravity. All I know...
  29. Emilyyyyyyyyy

    Calculate the impact force when falling from a height

    To find vx vx = dx/t = 3.86 m/1.5 s= 2.573 m/s To find Ek Ek = ½mvx²= ½(79.4)(2.573)²= 262.8 J W = FnetΔd Fnet = 262.8 J/ 3.86 m = 68 N He hits him with a force of 68N
  30. archaic

    Acceleration after applying a force

    Hello, 1) Suppose I throw a ball with a force ##F=ma##, the instant it leaves my hand, does it have the same acceleration ##a## added to it accelerations due to "ambient" forces (air resistance, gravity..)? 2) If I am right about 1), doesn't my hand already carry the acceleration/deceleration...
  31. A

    I Faking a Formula For Movement Through Gravity

    I have a strange question. It's strange because I don't need a correct answer. I need an answer that seems correct and leads to predictable results. I'm making a multiplayer computer game where the players fire cannons in outer space. The cannon shells will move through the gravitational fields...
  32. Avatrin

    Programming to learn kinematics

    Hi I am learning kinematics. Topics include inertia tensors, cosine matrices, quaternions, Euler angles etc... To learn these topics well, I want to try working on something a bit more difficult than just the underlying math. That will probably keep me more motivated. So, I am looking for...
  33. S

    Kinematic problem: velocity and stuff

    1. A stone is thrown vertically downwards from the observation deck of the CN Tower, 400 m above the ground, with a velocity of 12 m/s [down]. A) How long will it take the stone to reach the ground ? B) How fast will it be going when it hits the ground ? I just got into physics, so I’m not...
  34. D

    What is the maximum speed that an object must reach to satisfy minimum transit time?

    Hi, I need help with this problem: Homework Statement Condition: an object has to move from point A to point B in the least time possible. The distance between the points is L. The object can accelerate (decelerate) with a fixed acceleration ##a## or move with a constant speed. What maximum...
  35. K

    Baseball in the air 2D motion question

    Homework Statement A baseball is hit into the air, nearly vertically, with a speed of 27 m/s. When it comes down, the ballplayer catches it in his glove. Air resistance (drag) is actually fairly important for a baseball in flight, but for now let’s assume it is negligible. (a) How high...
  36. T

    Maximizing Transferred Energy between n bodies in linear collisions

    Homework Statement My problem has two parts. 1) We have two point masses ##m,M##. and there is another mass ##m_1## between them.They are all aligned in a line. Mass ##M## is moving with speed ##u_1## toward ##m_1## and after collision and all other masses are not moving. we want to find...
  37. E

    Relationship between ln k and 1/t using different formula

    Hi, I'm currently taking Chemistry 101 and came across this equation that seems to contradict what I've learned before. I don't know the name of it, but here is the equation and its implication. Now another equation we have learned is the Arrhenius equation, which is as follows: If I...
  38. Subrahmanyan

    Electrical Help finding appropriate equipment

    I would like to measure time period of very short periods of electricity flow in the range of micro seconds or even smaller;can someone tell me me a device that can help me do this?
  39. navneet9431

    Laws of motion while climbing a Rope

    I'm a little confused with the application of laws of motion on a man climbing a rope. Suppose a man of mass Mg is climbing a rope with an acceleration a. Rope is massless. Now if look through the frame of the piece of rope held by the man, there is a force Mg downward by man, ma downward...
  40. I

    Setting two expressions equal to each other

    Homework Statement Two cars are facing each other on a long straight airport runway. They are initially separated by a distance of 1 km. Car A begins to accelerate towards the other car at a uniform 0.5 ms^-2. Ten seconds later car B begins to move towards the other car with a uniform...
  41. A

    An electron & a proton are each placed in an electric field

    Homework Statement An electron and a proton are each placed at rest in an electric field of 687 N/C. What is the velocity of the electron 56.5 ns after being released? Consider the direction parallel to the field to be positive. The fundamental charge is 1.602×10−19 C, the mass of a proton is...
  42. devilish_wit

    I'm stuck! This is a combination of dynamics and free fall

    Homework Statement A flat cushion of mass m is released from rest at the corner of the roof of a building, at height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in the figure below. The air exerts no...
  43. devilish_wit

    I have a hard time with kinematics involving inclined planes

    Homework Statement Two blocks of mass m1 = 3.00 kg and m2 = 6.00 kg are connected by a massless string that passes over a frictionless pulley (see the figure below). The inclines are frictionless. Image - The inclined plane is shaped like a...
  44. C

    Raindrop free falling -- calculate the velocity and time

    Homework Statement Raindrops fall from a broken gutter at 1.0 s intervals to the ground , 19.6 m below Neglecting air resistance and taking g as 9.81 calculate the time for each drop to reach the ground velocity of the drops as they reach the ground speed of drop at the height of 14.7 m I...
  45. L

    Kinematics of a Car Crash

    Homework Statement "Based on the following data, determine if the driver who crashed was driving over the speed limit" The relevant data given is: -A 2002 Volvo t-bones a truck in an alley with a speed limit of 20km/h -An eyewitness heard tires screech, then a loud bang, and also said the...
  46. K

    Kinematics within a simulation

    Homework Statement I'm simulating a warehouse (in Unity) where forklifts and other vehicles transport stuff from point A to point B. The routes are modeled as a graph with vertices and edges. Every transport is saved as a task in a backend system with the relevant data such as starting time...
  47. L

    I'm having a comprehension issue with a 2-D motion problem.

    1. Problem Statement A 2 kilogram block rests at the edge of a platform that is 10 meters above level ground. The block is launched horizontally from the edge of the platform with an initial speed of 3 meters per second. Air resistance is negligible. The time it will take for the block to reach...
  48. V

    Circular motion

    Homework Statement A particle is moving parallel to x-axis in the positive direction with velocity v such that at all the instants the y -axis component of its position vector is constant and is equal to 'b'. Find angular velocity about origin. Homework Equations The Attempt at a Solution I...
  49. Cocoleia

    Position of particles on a detector after decay

    Homework Statement A hypertriton (a bound system with a L hyperon together with a deuteron core (proton and neutron) is produced at the origin of the coordinate, (x,y)=(0,0) with a velocity of 0.94c (beta=0.94), flying along the x-axis. The mass of the hypertriton is 2.991 GeV/c2 . It decays...
  50. AIshikrakshit

    Problem of projectiles

    Homework Statement Homework Equations $$h=ut+1/2at^2$$ $$h=x\tan\theta-1/2g\frac{x^2}{u^2\cos^2\theta}$$ The Attempt at a Solution I tried to take a random angle theta for the lower particee and then using the equation of the upper particle tried to solve them together and find condition for...