Linear motion Definition and 119 Threads

Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion with constant velocity or zero acceleration; and non-uniform linear motion with variable velocity or non-zero acceleration. The motion of a particle (a point-like object) along a line can be described by its position



x


{\displaystyle x}
, which varies with



t


{\displaystyle t}
(time). An example of linear motion is an athlete running 100m along a straight track.Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as gravity and friction can cause an object to change the direction of its motion, so that its motion cannot be described as linear.One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction. The analysis of such systems may therefore be simplified by neglecting the direction components of the vectors involved and dealing only with the magnitude.

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  1. 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:
  2. J

    How were these linear motion equations derived?

    how were these equations derived or found? x = xo + vot + 1/2at2I tried to use v=(xf-xi)/(tf-ti) and a=(vf-vi)/(tf-ti) but I don't know where the 1/2 comes from also this one: v2 = vo2 + 2a(xf-xi)
  3. V

    Linear Motion Integration Problem

    Homework Statement If the acceleration of a particle on a horizontal line is x where x represents the position in centimetres from the starting position of zero and if the initial velocity is 8 centimetres per second find the velocity of the particle when it is in a position of 15...
  4. C

    Comparing moment of inertia to mass in linear motion

    Homework Statement Compare the role played by the moment of inertia in rotational motion, to that played by mass in linear motion. Homework Equations I have no idea how to tackle this question. I tried looking up the defenition of moment of inertia as a start, but I only found anything...
  5. R

    Linear Motion: calculating height of cliff given speed of sound and time

    Homework Statement A student standing on top of a cliff drops a rock down below into the water and hears it splash 3 seconds later. The speed of sound is 330m/s, what is the height of the cliff Homework Equations v= d/t v2 = v1 + at d = v2-1/2 at2 d = (v1 + v2)t v2 squared = v1...
  6. G

    Converting unidirectional linear motion into rotary motion?

    Does there exist a device to convert a unidirectional linear motion into a rotational motion? I have only been able to find devices which do the exact opposite. I am probably missing out on some kind of key point here but I don't have much of a background in physics so please don't slam me too...
  7. P

    Linear Motion - Minimum Retardation to Avoid Crash?

    First post! I would be grateful if anyone could give me any advice on this particular type of problem (i.e min retardation to avoid a crash). I'm not necessarily looking for the answer to this specific question, I would rather if someone could point me in the right direction as to how to go...
  8. L

    Starting point in linear motion problem

    Hello all, I've been working my way through my homework this week, and haven't had much trouble until I hit this question... Homework Statement An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a...
  9. S

    What is the Velocity and Direction of a Puck on an Air Hockey Table?

    Homework Statement A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0 s, the x components of the puck's initial velocity and acceleration are v0x = +5.6 m/s and ax = +6.3 m/s2. The y components of the puck's initial velocity and acceleration are v0y =...
  10. S

    Converting Rotational Work to Linear Motion for a Crossbow

    I don't know if I'm using the terms properly, since I am no mechanical engineer, but I am attempting to find the best way to convert rotational work from an electric motor to draw a long, high-torque linear stroke, followed by a very fast return stroke. To clarify my question, I trying to...
  11. Femme_physics

    Dynamics circular and linear motion

    I wasn't even sure how to title this exercise since I don't really know how this movement is being officially called in English, I just called it "circular and linear motion" as a translation from Hebrew. Homework Statement http://img842.imageshack.us/img842/2149/xycoordinate.jpg The...
  12. Q

    Is Rotational Motion Possible in a Straight Line?

    can a body moving in a straight line be in rotational motion as well?
  13. E

    Help with Linear motion Question

    Homework Statement Heres is the problem I am trying to solve: George of the jungle, with mass m, swings on a light vine hanging from a stationary tree branch. a second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the opposite direction on it. Both...
  14. S

    Kinematics question (uniformly accelerated linear motion)

    Homework Statement Two friends see each other in a store and are initially 50m apart. The first friend starts walking towards the second at a constant speed of 0.50 m/s. At the same instant, the second friend accelerates uniformly from rest at a rate of 1.0 m/s^2 toward the first friend. How...
  15. E

    Linear Motion at Constant Acceleration Problem

    Homework Statement A cyclist starts at the top of a straight slope with an initial velocity of 3.00m/s. Five seconds later, she is at the bottom of the incline, having traveled 50.0m. Find her velocity at the bottom of the hill and her acceleration, assuming it to be constant. Homework...
  16. S

    Angular and Linear Motion problem

    Homework Statement Automobile Tire: If a car runs over a nail at 55 mi/hr and the nail is lodged in the tire tread 13 in. from the center of the wheel, then what is the angular velocity of the nail in radians per hour? Homework Equations w = alpha/time a = s / r The Attempt...
  17. G

    Basic linear motion question.Is it good?

    Homework Statement Airport runway designing: (i)lowest acceleration rate of any plane is likely to be 3m/s^2.Take off speed for this airplane will be 65m/s.what is minimum allowed length of runway? (ii)If airplane accelerates down runway at 3.2m/s^ for 32.8 seconds until it lifts...
  18. L

    Non linear motion ( Physics olympiads question )

    Homework Statement A cat sitting in a field suddenly sees a standing dog. To save its life, the cat runs away in a straight line with speed u. Without any delay, the dog starts with running with constant speed v>u to catch the cat. Initially, v is perpendicular to u and L is the initial...
  19. I

    Linear Motion - Particle Displacement

    The function v(t) = 9 - t2 is the velocity in m/sec for a particle moving along the x-axis, where t is measured in seconds (t is greater than or equal to 0). Use analytic methods to solve: (a) When the particle is moving to the right, to the left, and stopped. (b) The particles displacement...
  20. A

    Comparing Rotational and Linear Motion - block vs. disk vs. ring

    Comparing Rotational and Linear Motion -- block vs. disk vs. ring Homework Statement A disk and a ring, both of mass M and radius R, are placed atop an incline and allowed to roll down. A block, also of mass M, is placed atop the same frictionless incline and allowed to slide down. How do...
  21. B

    How to do error analysis in this lab on linear motion

    Okay so I did a lab on Linear Motion using the glider with the air track and a spacer. This is the information I have about the glider and spacer. glider mass = (468.7 +/- 0.02) g thickness of spacer =(14.8 +/-0.05) mm I'm stuck on doing the error analysis and I don't know how to go on...
  22. M

    Can Carnie Stop in Time to Avoid the Roadblock?

    OK This is a multi step problem that I really do not understand. Here it is: Carefree Carnie is driving her parents automobile on an autumn day. While driving with the cruise control set at 50 miles per hour, she notices a construction project's road block in her lane 60 meters ahead. If it...
  23. J

    Precise linear motion output from rotary input

    Hi, I need to get a precise linear oscillatory motion from a rotary input? Its for a compact carving tool. Any ideas on how to control the displacement? Thnks
  24. S

    Circular motion related to linear motion

    Homework Statement As block B moves upward with constant speed 2 m/s, pin A glides through the semicircular slot. At the position shown, determine the velocity of A. a. 2.31, angle 60o b. 2.00, angle 60o c. 1.00, angle 0o d. 1.89, angle 30o Homework Equations Not sure The...
  25. A

    What is the missing factor in this basic linear motion problem?

    Homework Statement A ball is thrown vertically into the air and is caught 3.1 seconds later. (This is just a basic linear motion question, so there are no 'advanced' considerations.) a) Find the velocity when the ball was thrown b) Find the max heightHomework Equations (Nothing really...
  26. S

    Lab Experiment - Uniformly Accelerated Linear Motion

    Hi there, I'm not sure if I'm posting in the right place or not... So please forgive if I am. I did an experiment today on Uniformly Accelerated Linear Motion. We used an Atwood's type machine that used pressurized air to reduce friction. We also used photogates to time the movement of the...
  27. W

    When Does the Car Overtake the Truck?

    Homework Statement A car is stopped at a red traffic light. At the instant the traffic light turns green, the car starts to move forward with a constant acceleration of 3.20 m/s2. At the same time as the light turns green, a truck traveling in the same direction with a constant speed of...
  28. S

    Obtaining xy-coordinate linear motion from angles of rotation

    Hello, I have a laser beam that passes through two 3 degree angled wedges, resulting in the ability to project the laser anywhere within a 6cm radius circle (each wedge alone produces a 3cm radius circle). I need to be able to tell each wedge how much to rotate in order to get the laser from...
  29. Run Haridan

    Acceleration. linear motion. i'm stuck

    acceleration. linear motion. I'm stuck! Homework Statement a train moves at a velocity of 60 m s-1 and stops after a distance of 600m. what is its deceleration?Homework Equations v=s/t The Attempt at a Solution this is my working: u= 0 m s-1 v= 60 m s-1 s= 600 m v=s/t 60=600/t t=10 s ...and...
  30. B

    Non Uniform Acceleration Linear Motion

    1st I am having problems getting a solution for final Velocity in terms of Distance traveled with a non-zero initial velocity. Acceleration = A / Velocity - B * Velocity^2 where A is a constant related to Hp (horsepower) of the vehicle and and B is a constant related to aerodynamic...
  31. T

    Equations of linear motion in terms of films

    Homework Statement I have been asked to investigate whether Hollywood is scientifically accurate. I decided to use a clip from speed where the bus jumps that hole in the road. I have worked out the speed in m/s from the dial on the bus (67mph = 28.87m/s) and the distance from what the guy...
  32. N

    Linear Motion to Angular Motion via an Impulse

    I am interested in how impulse turbines work. Supposing a mass of water (in kilograms), m, is expelled by a jet at a given velocity (in meters per second), v, its momentum (in Newton-seconds), p, is the product of these quantities: p = mv. Also, a paddlewheel’s angular momentum (in...
  33. N

    What is the maximum reaction time to avoid hitting the deer?

    A ranger in a national park is driving at 28.0 mi/h when a deer jumps into the road 155 ft ahead of the vehicle. After a reaction time t, the ranger applies the brakes to produce an acceleration of a = -9.00 ft/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer...
  34. T

    How Do You Calculate Acceleration and Maximum Height in Linear Motion Problems?

    Homework Statement 2 linear motion problems hi i have 2 questions on linear motion that i could use some help on step by step. 1. Jules Verne in 1865 proposed sending men to the moon by firing a space capsule from a 220-m cannon with final velocity of 10.97 km/sec.. What would have been...
  35. T

    What Are the Calculations for Acceleration in These Linear Motion Problems?

    Homework Statement 2 linear motion problems -------------------------------------------------------------------------------- hi i have 2 questions on linear motion that i could use some help on step by step. 1. Jules Verne in 1865 proposed sending men to the moon by firing a space...
  36. T

    What Is the Unrealistic Acceleration in Jules Verne's Moon Launch Scenario?

    hi i have 2 questions on linear motion that i could use some help on step by step. 1. Jules Verne in 1865 proposed sending men to the moon by firing a space capsule from a 220-m cannon with final velocity of 10.97 km/sec.. What would have been the unrealistically large acceleration...
  37. R

    Can Acceleration and Motion Principles Solve These Physics Problems?

    Homework Statement 1.Two runners accelerate from rest with the acceleration of runner A twice that of runner B. After accelerating for a given time, the speed of runner A will be twice that of runner B. is this right or wrong? 2.An ball is thrown vertically upward. At the top of its...
  38. C

    What is the slope of the ground in the landing zone?

    [SOLVED] linear motion Homework Statement Skiers leave a ski jump at 28 m/s, at an angle of 9.5 degrees below the horizontal. Their landing zone is a horizontal distance of 55 m from the end of the jumo The ground is contoured at that point so that the skiers trajectories make an...
  39. A

    Solving a Linear Motion Question: Two Cars, 70km & 4.4m/s & 2.5m/s

    i have a problem solving a linear motion question, this is the question two cars moving in a straight line of 70km with velocities 4.4m/s and the other 2.5m/s. when will they meet if a) they moved towards each other b) they moved in the same direction.
  40. S

    What Causes a Body to Move in a Straight Line?

    Homework Statement what is/are for a body to move in a straight line? Homework Equations The Attempt at a Solution
  41. P

    What Is the Speed of Water Leaving the Nozzle?

    Homework Statement You adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically upward at a height of 1.5m above the ground. When you quickly move the nozzle away from the vertical, you hear the water striking the ground next to you for 2.0 s. What is the...
  42. C

    Solving Linear Motion: Car Acceleration

    [SOLVED] linear motion Homework Statement A car enters a turn at 85 km/h, slows to 55 km/h, and emerges 28 s later at 35 degrees to its original motion, still moving at 55 km/h. What is the magnitude an direction of the average acceleration measure with respect to the car's original...
  43. T

    Uniformly Accelerated Linear Motion

    [SOLVED] Uniformly Accelerated Linear Motion Hello, I am attempting what looks to be a fairly easy problem involving uniform acceleration and linear motion, but my answers just aren't coming out right and I'm unable to see where I'm going wrong. Any help is appreciated. Homework Statement...
  44. S

    Linear Motion -Velocity and Acceleration

    Linear Motion --Velocity and Acceleration Homework Statement [10] A toy car travels along a straight line. Its position x varies with time as shown on the x-t graph. The equation of motion in the A-C interval is given by x(t)=alpha+(beta)t^2+y(t)^(1/2) where alpha=1.0 m, beta=1.3 m/s^2...
  45. C

    Solving Linear Motion: Bird Catching Fish

    [SOLVED] linear motion Homework Statement A bird is flying 30 m above a lake when it drops a fish. Another bird at 35 m immediatley dives and catches the fish before it hits the water. What is the initial velocity of the second bird? [b]2. Homework Equations h=h0 +...
  46. I

    Optimizing Traffic Flow with Collision-Avoidance Automated Control Systems

    According to a Scientific American article, current freeways can sustain about 2400 vehicles per lane per hour in smooth traffic flow at 96 km/h (60 mi/h). With more vehicles the traffic flow becomes "turbulent" (stop-and-go). a) If a vehicle is 4.6 m (15ft) long on the average, what is the...
  47. C

    Projectile Motion and linear motion problem

    A projectile is launched at an angle α from the edge of a cliff of height H above sea level. If it falls into the sea a distance D from the base of the cliff, prove that its maximum height above sea level is H + [(Dtan α)^2]/4(H + Dtan α) Newtons equations of linear motion in the i/j...
  48. V

    Conceptual Q - Rolling Resistance, Angular + Linear motion -const. acceleration

    Hello, new poster here. I have trouble understanding some friction/resistance properties and how they are applied to rolling & linear motion simultaneously. I've done a lot of simple static / dynamic (sliding) friction examples as well as rolling without taking into account resistance, but...
  49. B

    Solving Linear Motion from Voltage and PE/KE

    Homework Statement So I suck at physics, especially when it comes to going from one thing to another, in this case Voltage and PE/KE to linear motion. Anyways here's the question, any hints as to how I should go about to solve it would be much appreciated A point charge of -10nC is at the...
  50. C

    Rotation and Linear Motion BonuS Help

    1. Homework Statement A system consists off two small disks of masses m and 2m that are on a plane. The length that connects the two mass is of negligible mass is is 3L long. The rod is free to rotate on a vertical axis P and the mass 2m lies L away from P and the mass m lies 2L away from P...
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