What is Kinematics: Definition and 1000 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. L

    Tough Physics integration problem dealing with kinematics.

    Homework Statement A train traveling at v0 = 22.0 m/s begins to brake by applying a velocity-dependent instantaneous acceleration a(v) = α /(v + u) m/s2, where α = – 23.0 m2/s3, v is the instantaneous velocity of the train, and u = 0.5 m/s. Determine the distance traveled by the train until it...
  2. J

    Calculating Distance for a 15 Minute Lead: Kinematics Question Explained

    Homework Statement Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70.0 mi/h. How far must the faster car travel before it has a 15 minute lead on the slower car? Homework Equations average velocity=change of...
  3. M

    Kinematics Questions: Solutions and Explanations

    Can you answer this for me pls? I need this tomorrow and I still have so much work in hand. This questions are about Kinematics. pls help me. with solutions pls :) • The World Trade Center and the Empire State Building in the “Big Apple” have heights of 417 m and 381 m respectively. If...
  4. P

    Kinematics in 2 dimensions; position vector problem.

    Homework Statement "A particle moves in the horizontal plane that contains the perpendicular unit vectors i and j. Initially it is at the origin and has velocity 18ims^-1. After accelerating for 10 seconds its velocity is (30i + 8j)ms^-1. Assume that the acceleration of the particle is...
  5. A

    Kinematics- police driver acceleration problem

    In an accident investigation police measured the skidmarks left my vehicle. they measure the skidmarks to be 150 m from the point where the driver applied the brakes to where the car came to rest. In their investigation the police Sumat the driver was traveling at this bead limit of 80 km/h...
  6. J

    How Many Meters Did You Win the Race By?

    Homework Statement You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win? Homework Equations vavg=Δx/Δt v=x/t The Attempt at a Solution I have the answer already with the...
  7. M

    Kinematics truck moving at 30m/s suddenly notices a moose 70m

    Homework Statement The driver of a truck moving at 30m/s suddenly notices a moose 70m straight ahead. If the driver's reaction time is 0.5s and the maximum deceleration is 8m/s^2, can he avoid hitting the moose without steering to one side? The Attempt at a Solution First I found out how...
  8. M

    Kinematics A car moving at 60km/h meets a train of length 1km

    Homework Statement A car moving at 60km/h meets a train of length 1km moving at 40km/h along a track parallel to the road. What distance does the car travel in passing the length of the train given that they travel a) in the same direction, or b) in opposite directions? Homework Equations...
  9. Y

    What is the Kinematics Problem for a California Condor Carrying Carrion?

    A California Condor is approaching its nest with a large chunk of carrion in its beak. As it approaches, it makes an upward swoop, achieving a momentary upward velocity of 12.8 m/s when the carrion falls from its mouth, hitting a cliff outcropping 32.1 m below. Determine the speed of the carrion...
  10. R

    A few Angular Momentum and Rotational Kinematics Conceptual Questions

    Homework Statement Each of the questions are either increase, decrease, equal, or undetermined. 1) You are sitting on a rotating chair, holding a 2 kg mass in each arm outstretched. When the masses are dropped, your angular momentum -------. 2) You sit in a rotating chair holding 2 kg...
  11. A

    Rigid body kinematics problem: finding the velocity of the center of mass

    I have to deal with the problem of finding an expression for the kinetic energy of a rigid body. One of its point is pivoted to a point that moves arbitrarily. So in order to find an expression for the kinetic energy I use König's theorem, but I need the velocity of the center of mass. I use...
  12. H

    Kinematics - Acceleration equation confustion

    Kinematics -- Acceleration equation confustion I have been following a derivation and can't quite wrap my head round what is happening. I don't know if the person who wrote it has made a mistake somewhere or I am making the mistake. I am informed that a = \frac{dv}{dt} Fine. Then I am told...
  13. B

    Can Kinematics Equations Be Used for an Entire Projectile Trajectory?

    I feel like I'm missing a large concept of the kinematics equation. Up until today, I have only used them for HALF of a trajectory (initial velocity and final velocity of 0 at the apex). But can you use them for an ENTIRE trajectory? So say something is fired from the ground and lands on the...
  14. F

    Solve Kinematics Problem: Car Overtaking Truck

    I need help with this problem. Any help is greatly appreciated. Homework Statement At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.40m/s^2 . At the same instant a truck, traveling with a constant...
  15. J

    How Does Constant Acceleration Affect Distance Traveled?

    A car accelerates at 3 meters squared from rest for 10s. How far does it travel? a = 3 meters squared v1 = 0? v2 = ? Δd = ? Δt = 10s Why is velocity 1, 0? Why is delta t 10 seconds?
  16. S

    Physics kinematics calculus question

    Homework Statement Initial acceleration of a particle moving in a straight line is a° and initial velocity is zero. The acceleration reduces continuously to half in every t° seconds. What will be the terminal velocity(v)?Homework Equations \intadt=\intdvThe Attempt at a Solution...
  17. M

    Problem concerned to kinematics

    Homework Statement A body standing on a bridge throws a stone vertically upwards with a velocity of 20 m/s. it strikes the water below after 3 seconds, the height of the bridge over the water level in the river is : a. 45 m b. 10 m c. 5 m d. 15 m Homework Equations vf^2= 2aS +...
  18. M

    Problem concerned to kinematics

    The percentage errors in the measurement of mass and speed are 2 % and 3% respectively.how much wil be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed? its ans is 8 % .. according to this equation K = mv^2/ 2 , so dK / K = dm/m + 2dv / v ( d means...
  19. S

    Tarzan Physics Question with Kinematics, Energy, Forces

    Homework Statement Tarzan (63.0 kg) is trying to save Jane (50.0 kg) from the fast approaching crocodile (who is in the crocodile pit). Tarzan starts from rest at point A and swings off the edge of a cliff 30.0 m above the ground, while hanging on to a vine of a very large tree. At point B...
  20. T

    Special Relativity and Kinematics Problem

    Homework Statement There are three particles along the x-axis ordered from back to front, A, C, B. A travels at 4/5c and B travels at 3/5c, the speed of particle C is unknown. What must the speed of particle C be such that A and B will arrive at C at the same time? And, at what speed will both...
  21. V

    Physics Kinematics Question (Check my work?)

    Physics Kinematics Question! :) (Check my work?) Homework Statement A ball is thrown vertically up from a window that is 3.6 meters above the ground. The ball's initial velocity is 2.8 m/s up. What is the ball's velocity when it hits the ground? How long after the first ball should a second...
  22. sankalpmittal

    Question regarding kinematics : motion in one dimension.

    Homework Statement The velocity of particle is 0 at t=0. Then , (a) The acceleration at t=0 must be zero. (b) The acceleration at t=0 may be zero. (c) If the acceleration is 0 from t=0 to t=10 s , the speed is also zero in this interval. (d) If the speed is 0 from t=0 to t=10 s...
  23. U

    1-D Kinematics Problem/Free Fall. A helicopter carrying Dr. Evil

    1-D Kinematics Problem/Free Fall. "A helicopter carrying Dr. Evil..." NOTE: I'm new here and I wanted to make sure I am not breaking the rules: I show most of my work step by step for this problem since there are so many things going on in it. My question is whether or not my though process is...
  24. N

    Kinematics Equation Help: Calculating Runner's Acceleration for 10,000m Run

    A runner hopes to complete the 10,000m run in less than 30.0 minutes. After exactly 27.0 minutes, there are still 1100m to go. The runner must then accelerate at 0.20m/s^2 for how many seconds in order to achieve the desired time. I have calculated the runner moving at 5.5m/s^2 for the...
  25. C

    Why does this kinematics problem seem impossible.HELP

    why does this kinematics problem seem impossible.HELP! Homework Statement If the man's mass is 70 kg, if L is 0.4 m h is 0.6 m, what is the downwards force (assumed constant) exerted by his feet during the phase A to B? State any physical law or principle you use in obtaining your answer...
  26. M

    A few quick problems with kinematics

    Hi there, Sorry for so many questions, but I feel frankly stupid for getting these wrong, and yet I have no clue why they're so off. Any ideas of why the answers are what they are? Thanks so much. 15. A truck starts from rest and accelerates at 1.5 m/s2for 20 s. It then travels at constant...
  27. P

    How Fast Must the Hammer Move to Ring the Bell at the Carnival?

    Homework Statement At a carnival, you can try to ring a bell by striking a target with a 9.00 kg hammer. In response, a 0.400 kg metal piece is sent upward toward the bell, which is 5.00 m above. Suppose that 25.0% of the hammer's kinetic energy is used to do the work of sending the metal...
  28. P

    Work-Energy Kinematics skier

    Homework Statement An extreme skier, starting from rest, coasts down a mountain that makes an angle of 25.0° with the horizontal. The coefficient of kinetic friction between her skis/snow is 0.200. She coasts for a distance of 10.4 m before coming to the edge of a cliff. Without slowing down...
  29. Hepth

    3 Body Decay Kinematics (Width Calc): Examples?

    Does anyone know of any worked out examples for the calculation of the width of a 1->3 decay process, where ALL THREE masses are included? I can find a LOT of examples where they let the masses go to zero, (like leptonic/semi leptonic decays, decays to pions, etc). This makes the integrals...
  30. F

    Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

    Homework Statement An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east. (A) Determine the ground speed. (B) Determine the direction of motion of the plane, expressed as an angle...
  31. X

    Finding the Minimum Distance Between Two Points Using Graphing Calculator

    Homework Statement Two points P and Q have position vectors in a reference frame that are given by rOP = 50ti and rOQ = 40i - 20tj meters. Find the minimum distance between P and Q and the time at which this occurs. Homework Equations The Attempt at a Solution I suppose I take the...
  32. L

    Kinematics problem with constant acceleration

    A ball is thrown downwards from a top of a 20m building with an initial velocity of 15m/s. What equation could be used to model its height? My answer: h (t) = -4.9t2-15t+20
  33. J

    Simple block kinematics problem

    Homework Statement Block A weighs 75lbf and the coefficients of static and kinematic friction between A and the plane are both 0.50. Determine the acceleration of A under the action of the 25 lbf force when the velocity at A is (a) 8fps up the plane, (b) 15 fps down the plane. (c) Zero...
  34. F

    Kinematics of Linear Motion: Solving Problems with Constant Acceleration

    Homework Statement I am unable to solve part b and please help me check whether is there anything wrong with my graph..:redface:The Attempt at a Solution Segment A Vi=0 V=3 S=60 a=9.81 v=vi+at 3=0+9.8(t) t=0.305s Segment B Vi=3 V=0 a=-2 v=vi+at 0=3-2t t=1 t=1+0.305=wrong answer :cry:
  35. R

    Robotics kinematics help, rotation, velocity, acceleration, jerk

    Homework Statement The question is: "The wheel kinematic constraints derived in section 3.2.3 of the book assume that the wheel does not skid (equation 3.12) or slide (equation 3.13). These assumptions are unrealistic in many situations, such as on the surface of Mars or on the DARPA Grand...
  36. F

    Kinematics of Rotational Motion Part II

    Homework Statement I cannot get the answer for part c, -13.02rad/s^2 The Attempt at a Solution 52.08=260.42+α(10) -208.34=10α α= -20.83rad/s^2 (Correct) 0=52.08+α(10) -52.08=10α α=-5.208rad/s^2 (Wrong) Please help, thanks..
  37. F

    Kinematics of Rotational Motion (Gears)

    Homework Statement Since Gear A -------- Vi=0 t=12s θ=40∏ as given in the question, can I assume that Vi=0 t=12s for Gear B/Drum C as well? If not why? Thanks..
  38. D

    Kinematics of Rigid Bodies question

    Homework Statement The uniform 3.6m pole is hinged to the truck bed and released from the vertical position as the truck starts from rest with than acceleration of 0.9m/s^2. If the acceleration remains constant during the motion of the pole, calculate the angular velocity of the pole as it...
  39. J

    What is the required speed for the last 2 laps to qualify for the race?

    Homework Statement "A race car driver must average 180 km/h for 4 laps to qualify for a race. Because of engine trouble, the car averages only 150 km/h over the first 2 laps. What speed must be maintained for the last 2 laps?" Homework Equations The Attempt at a Solution So I do...
  40. T

    Max Accel of Object: Can't Find Solution?

    Homework Statement This problem seems so simple yet I don't feel there is enough information to know what is the maximum acceleration the object can travel at without tipping over. I uploaded a picture of the object along with the variables. rope AB = 6 ft Angle of AB = 78 degrees...
  41. G

    Design a Toy with Kinematics: Get Creative

    As part of a culminating activity for my course, I am asked to design and build a toy for children that uses kinematics and conservation of energy. I was wondering if anybody could post some ideas?
  42. B

    Should I Attempt the Pass? Kinematics Problem on a Car

    Homework Statement A car is behind a truck going 25 m/s on the highway. The car's driver looks for an oportunity to pass, guessing that his car can accelerate at 1.0 m/s^2. He gauges that he has to cover the 20 m length of the truck, plus 10 m clear room at the rear of the truck and 10 m at the...
  43. X

    What Angle Should the Archer Shoot the Arrow for Optimal Accuracy?

    Usually these problems are really simple for me, but this one is making me lose my mind: "An archer wishes to shoot an arrow at a target at eye level a distance of 49.0 m away. If the initial speed imparted to the arrow is 69.3 m/s, what angle should the arrow make with the horizontal as it is...
  44. C

    Check work on kinematics problem

    Homework Statement A truck accelerates uniformly from rest to 48km/h in 20s, holds speed for 2 minutes, and then accelerates to 100km/h at a rate of 17m/s^2. How long does it take, from rest, to reach 100km/h and what distance it traveled in this time? The book says it takes 148.5s, and I...
  45. M

    Help on a kinematics (possibly) question ?

    Homework Statement See attached picture please. It is supposed to be a pully system with 100N being applied upwards and i need to prove the values given in the diagram i drew and my teacher gave me it as a question to do since we have finished the scottish higher course. Homework Equations...
  46. Femme_physics

    Kinematics problem - struggling with my calculus

    Homework Statement http://img62.imageshack.us/img62/6705/smallproj.jpg The Attempt at a Solution Basically I'm struggling to understand what am I supposed to differentiate. If it's V, which is 60, then the derivative of a number is zero. If it's a, then, a = -1.2v2 If I am...
  47. I

    Kinematics: Understanding Acceleration and Deceleration - Questions 7 and 11

    Question 7 a) Acceleration is the rate of change of velocity Use your definition in (a) to show that v = u + at, where v is the final velocity, u is the initial velocity and a and t are the acceleration and the time interval respectively. State the conditions that must be satisfied for...
  48. N

    Newtons second law and kinematics

    1)A rock is dropped off a cliff and falls the first half of the distance into the ground in t1 seconds. If it falls the second half of the distance in t2 seconds, what is the value of t2/t1? Relevant equations: I think the kinematics equations of d=vt+(1/2)at^2 I have no idea how to solve...
  49. M

    1 mark question on kinematics, or a stone fallin through air.

    Homework Statement A stone is dropped from the top of a tower of height 40 m. The stone falls from rest and air resistance is negligible. What time is taken for the stone to fall the last 10m to the ground? A 0.38s B 1.4s C 2.5s D 2.9s Homework Equations The Attempt at a...
  50. Y

    Kinematics of Rigid Bodies in 3D

    Homework Statement Problem 15.18: I've defined the positive J (fixed) axis along the pole pointing upwards and the positive X (fixed) axis going to the right, with both centered at the point of contact between the hoop and the pole, which I will refer to as point O. The rotating axes...
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