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.
Homework Statement
Displacement of a particle moving in a straight line is
s= 6 + 12t - 2t^2
find the distance traveled till t=5.
Homework Equations
firstly i am having confusion in correctly interpreting the equation. The equation gives us the displacement in 't' th...
Homework Statement
using a map, measure the displacement from Bradford to Milton. Compare the distances traveled to the for each route above with this displacement and explain the differences
Homework Equations
Δd = vΔt
The Attempt at a Solution
okay, so i may just being having a brain fart...
Homework Statement
Hello, i am trying to achieve inverse kinematics of a spherical manipulator (three revolutes in orthogonal axes) and the first angle (from geometry) is determined by something like this θ1=atan2(x,y) (i use maple so the function is something like θ1=arctan(y,x)); when i...
Homework Statement
Base ball player makes perfect contact with a ball striking it at 45° angle above the horizontal at a point 1.3 m above the ground. His ball just makes it clear of the 3m wall 130m from home plate. What was the velocity at with he struck the ball.
Homework Equations
is...
Kinematics -- marbles rolling down a ramp and into sand
Homework Statement
14) The student carries out an experiment to investigate momentum and collisions. A ball bearing is rolled down a ramp clamped at the edge of a bench. The ball bearing makes a head-on collision with a marble at the...
Homework Statement
A wheel starts from rest and accelerates uniformly to 200rpm in 6s. After it has been rotating for some time at this speed, the brakes are applied and it takes 5 minutes to stop the wheel. If the total number of revolutions is 3100, calculate the total time of rotation...
Homework Statement
A speeder zooms past a parked police car at a constant speed of 70 mph. Then, 3 sec later, the policewoman starts accelerating from rest at 10 ft/s^2 until her velocity is 85 mph. How long does it take her to overtake the speeding car if it neither slows down nor speeds...
Homework Statement
Jack is driving with a pail of water along a straight pathway at a steady 25 m/s when he passes Jill who is parked in her minivan waiting for him. When Jack is beside Jill, she begins accelerating at the rate of 4.0 x 10-3 m/s2 in the same direction that Jack is driving...
Please forgive me if the answer to this question is obvious, I studied Political Science for three years in undergrad before I realized 'real' science was far more rewarding.
My question (not homework):
I understand that Work-Energy can be used for projectile motion, if what you're after is...
Homework Statement
at the instant the traffic light turns green, an auto mobile starts with a constant acceleration of 2.2 m/s^2. At the same instant, a truck traveling with a constant speed of 9.5 m/s overtakes and passes the car.
a) how far beyond the traffic signal will the auto mobile...
Homework Statement
A point Q in rectilinear motion passes through the origin at t=0, and from then until 5 seconds have passed, the acceleration of Q is 6 ft/s^2 to the right. Beginning at t = 5s, the acceleration of Q is 12t ft/s^2 to the left. If after 2 more seconds point Q is 13 feet to...
Homework Statement
Figure 2-21 shows a general situation
in which a stream of people attempt to escape through an exit door
that turns out to be locked. The people move toward the door at
speed vs 3.50 m/s, are each d 0.25 m in depth, and are separated
by L 1.75 m.The arrangement in...
1. A particle of mass m moves on the x-axis as follows. It starts from rest at t=0 from the point x=0 and comes to rest at t=1 at the point x=1. No other information is available about its motion at intermediate times (0<t<1). If α denotes the instantaneous acceleration of the particle, then...
Homework Statement
So, our lab entails the students launching a projectile at a certain angle into a cup at a certain distance away. The launcher is 37 cm off of the ground and the cup is 7cm of the ground, so the Dy = 37-7 = 30cm. We will be given the angle in class and will be asked to...
Homework Statement
A one stage booster rocket has a Xo of 0m and a Vo of 0 m/s. The rocket takes off with a constant acceleration until 5 seconds when the boosters turn off and goes into free fall. The rocket is set to explode the instant it hits it's max height. The max height is 1200m...
Homework Statement
A 5.0kg concrete block accelerates down a 34° slope at 4.2m/s^2. Find the coefficient of friction between the block and the slope.
Homework Equations
Fg=5*9.8=45
x=45sin30
y=45cos30
The Attempt at a Solution
a=(mgsinθ-Ff)/m → Ff=mgsinθ-ma
Thanks
Homework Statement
Dr. Evil runs out to his car which is parked at the bottom of a hill that is inclined with the horizontal at 20(degrees) and blasts up the hill at an acceleration of 6 m/s2. James Bond runs out behind Dr. Evil to a mortar that is located conveniently exactly where Dr...
Homework Statement
Emily and Grace are each in a bumper car facing each other 10m apart. Emily moves toward Grace at a constant speed of 2.5 m/s. Grace accelerates toward Emily at a rate of 0.5 m/s^2. Relative to where Emily started, where do the two bumper cars collide?Homework Equations...
Homework Statement
A bird is coasting along in an easterly direction at 0.447 meters/sec when a strong wind from the south imparts a constant acceleration of 0.300 m/s2. If the acceleration from the wind lasts for 2.70 s, find the magnitude, r, and direction, θ, of the bird's displacement...
Check my "Throw the Ball" lab. (2D kinematics, force, work)
Here I have a lab, with explanation, questions and my worked out answers (tried to make it as neat as possible with all the formulas I use, lowercase letters are subscript letters). Can someone carefully check my math for all this? I...
Kinematics Train Crash Question
Homework Statement
A passenger train is behind a freight train, both on the same set of tracks and moving in the same direction. The freight train is moving at a constant speed of 27. 0 m/s and maintains that speed. The passenger train is originally moving at...
Homework Statement
A daredevil is shot out of a cannon at 33.7◦ to the horizontal with an initial speed of 25.5 m/s. A net is positioned at a horizontal distance of 43.7 m from the cannon from which the daredevil is shot.
The acceleration of gravity is 9.81 m/s^2
At what height above the...
Homework Statement
Hey guys, so here's the problem I'm given:
You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the...
Homework Statement
In an emergency braking exercise, a student driver stops a car traveling at 83 km/h [W] in a time of 4.0 s. What is the car's acceleration during this time?
Homework Equations
The Attempt at a Solution
a = (v2-v1)/t
= 83/4
= 21 m/(s^2) [E]
Homework Statement
A particle moves uniformly with speed v along the path y=kx^2 .Taking k as a positive constant, acceleration of the particle at x=0 is _________?
Homework Equations
options-a)2kv^2 b)kv^2 c)1/2(kv^2) d)2kv
The Attempt at a Solution
I did- y=kx^2...
Homework Statement
Rock A is thrown straight up from the top of a 25m tall building at a speed of 20m/s. Exactly 1 second later Rock B is thrown in such a way that it lands on the ground at the base of the building at the same instant that Rock A lands. What is the initial velocity for Rock...
a motorcycle starts from rest point A and travels 300m along a straight horizontal track to point B where it comes to a stop. if the acceleration is limited to 0.7g and deceleration to 0.6g calculate the least possible time to cover the distance and maximum velocity reached.
Can anyone point...
Homework Statement
A koala throws a eucalyptus branch. It goes 1.5 meters. If it left at 43 degrees, what velocity did the branch have when it left the koala's paw?
The answer must be in vector form (m/s @ degrees).
Needed: initial velocity
Known:
x-displacement = 1.5m
x-acceleration =...
Homework Statement
A particle moves along the x axis. It is initially at the position 0.250 m,
moving with velocity 0.200 m/s and
acceleration -0.290 m/s2.
Suppose it moves with constant acceleration for 5.80 s.
Position of Particle after 5.80 Seconds - -3.4678 m.
Velocity of Particle...
alright so here's a pretty straight forward question asking to find the avg acceleration:
A car with a velocity of 25m/s [E] changes its velocity to 25 m/s [s] in 15s. Calculate
avg acceleration.
So i drew out the vector diagram, found the resultant velocity and solved for the avg...
Homework Statement
Two people start from rest at 88m apart and walk directly toward each other. Person A has a magnitude of .3m/s^2, while person B has a magnitude of .2m/^2. Relative to person A's starting point, where do the people coincide?
Homework Equations
How to determine...
Homework Statement
The figure below represents part of the performance data of a car owned by a proud physics student. (The horizontal axis is marked in increments of 1 s and the vertical axis is marked in increments of 1 m/s.)
Here's a picture:
http://i.imgur.com/6bGXd.png
(d)...
Homework Statement
Two train cars are on a straight, horizontal track. One car starts at rest and is put in motion with a constant acceleration of 2.1 m/s2. This car moves toward a second car that is 25 m away and moving at a constant speed of 3.6 m/s.
(a) Where will the cars collide...
Homework Statement
Here is my question: A crane is moving a stainless steel coil weighing 497.3 slugs. The crane's cable snaps and the coil falls for 3/4 seconds before hitting the ground. What is the FORCE the coil hits the ground with?
Homework Equations
F=ma
PE=KE??
The...
1. A uniform rigid rod of length L and mass M is attached to a frictionless pivot point at one end. The rod is initially held completely horizontal and is released from rest. What is the linear and angular velocities at the instant the rod is in the vertical position?2. -ΔU = ΔK
3. -ΔU =...
Homework Statement
A baseball is thrown downward from a 12.5m tower with and initial speed of 4.5m/s. Determine the speed at which it hits the ground and the time of travel.
s = 12.5m
u = 4.5m/s
a = g = 10m/s^2
Homework Equations
Motion equations used
s = ut + 0.5at^2
v^2 = u^2 +2as...
Homework Statement
A car, traveling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car starts to accelerate in the same direction as the speeding car. What is the speed...
Homework Statement
A massless spring with sprint constant k is vertically mounted so that bottom end is firmly attached to the ground, and the top end free. A ball with mass m falls vertically down on the top end of the spring, becoming attached, so that the ball oscillates vertically on the...
Homework Statement
1.A block is sent up a frictionless ramp along which an x-axis extends upward. The figure below gives the kinetic energy of the block as a function of position x; the scale of the figure's vertical axis is set by Ks = 38.0 J. If the block's initial speed is 4.70 m/s, what is...
Homework Statement
A ball is thrown straight up. At the top of its path its instantaneous speed is
a) 5m/s
b) 20m/s
c) 50m/s
d) 10m/sHomework Equations
The Attempt at a Solution
Homework Statement
Let's say an object is moving with x(t)= e^(-1/t^2)
it's motion is continuous everywhere and differentiable because its exponential
so v(t)= 2e^(-1/t^2)/t^3
a(t)= e^(-1/t^2) *(4-6t^2)/t^6
I have asked to a calculus teacher and he said all the derivatives will be 0 at...
Homework Statement
My physics classes were a long time ago, and I can't for the life of me remember how to solve this problem: If I have two spheres s1 and s2 touching, of mass m1 and m2, with radii r1 and r2, and centers c1 and c2, and I have a force Fout normal to the surface of s1, how do I...
I'm really lost on how to do this physics problem because I don't really understand all the components of the problem:
A 7.25 kg block is sliding at 5.45m/s on a frictionless lab bench which is 8.6m high. The block hits a 1m "rough patch" before sliding off of the lab bench, and then lands...
Homework Statement
Okay so here is the problem: A golf ball is struck and leaves the ground at 96 m/s on a 60 angle. Determine the velocity of the ball 2 seconds after it was struck. I have the answer provided, which is 32.6 m/s at 45° above the horizon.
Homework Equations
Obviously I...
Homework Statement
In another universe, the force of gravity causes not a constant acceleration, but a constant "jerk" (third derivative of position with respect to time) with a value of j in the downward direction. An object is launched from the ground with an initial velocity of v_0 at an...
Homework Statement
A trolley is released from rest from the top of a runway which is 8m long. The displacement, s in metres, of the trolley is given by the expression(see below) where t is in seconds. Using calculus initially determine (a) an expression for the velocity of the trolley (b) the...
Homework Statement
the question is:
A 62 kg person in an elevator is moving up at a constant
speed of 4.0 m/s for 5.0 s. T / I C
(b) Calculate the work done by the normal force on the person.
(c) Calculate the work done by the force of gravity on the
person.
(d) How would your...
Homework Statement
This is a multi-choice question in one of the past papers I'm doing in preparation for my upcoming exam. All info is provided in the picture attached.
Homework Equations
SUVAT Equation most likely apply, but unsure how to go about it.
The Attempt at a Solution...
Homework Statement
A penny with mass of 3.1 grams is dropped from skyscrapper of height 1250m. Find the objects acceleration after 5 secs. If a penny with mass 2.5g is dropped at this point how far does it travel before the first penny hits the ground?
Homework Equations
Kinematic...
Homework Statement
Farhana is late for class and she is ready to do anything to get to school on time. She knows a mattress truck passes her balcony exactly at 8:42 a.m, traveling at a constant 40km/h. If her balcony is 8.21m from the ground and the truck has a height of 3.47. How far must the...