# What is Linear motion: Definition and 119 Discussions

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. ### Graph of time vs distance for sizing a motor for linear motion

Hi, I'm sizing motor for a linear motion, usually for the time distance graph would be looks like this, however, how does the graph look like if the stroke is very short? Example: velocity is 0.1m/s, acceleration is 1m/s2, moving stroke is 0.5mm, a cycle is within 0.05s the application is to...
2. ### B Rotation is absolute, linear motion is relative?

Can you explain with example what mean rotation is absolute and linear motion is relative?
3. ### Cam forces acting on a linear motion bearing with nonlinear forces

I have a machine I am designing that for all intensive descriptions, is a simple press designed to compress loose product into a puck like shape. The press force comes from a roller bearing mounted to a piston shaft, the rod sliding through a rigid linear bearing and the piston on the end of...
4. ### Uniformly accelerated linear motion downwards

Could you check if what I did is right and help me at e) and f)? Thank you!
5. ### How Do You Calculate Race Car Acceleration and Power Output?

A new development race car of mass 400 kg accelerates from 20 km/h to 200 km/h over a distance of 120 metres. Frictional and wind resistance forces can be assumed to be 1000N during the acceleration. Determine the following: (i)The average acceleration from 20 km/h to 200 km/h (ii)The time...
6. ### Linear motion, motorcyclist braking time

I tried using equations listed above to get the answer, but I get stuck with a and Vi. What am I doing wrong? The answer is 6.7 seconds.
7. ### Rotation around a non fixed axis + linear motion of a system

I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...
8. ### Linear Motion and Linear Momentum

Linear Motion Equation to get the common velocity of the block and bullet just after collision: v2=u2+2gs, I set v=0 at max height of s = 0.004 m and g = -9.81 m s-2 I got u = 0.28 m/s Then I calculate the impulse of the block using formula J = mv - mu, where v=0 and u=0.28 m/s and I got J = 1.4...
9. ### Calculating Force and Torque for Linear motion (image provided)

This is how I understand the torque (T1) created at the axis of rotation due to the spring would be calculated. This is considering the spring is starting from a fully extended state and is not already compressed. This is considering that (A) has a distance of 2 in. and the force from the spring...

11. ### Some quick questions concerning uniform acceleration and linear motion

Hello, I hope you are all having a great day ! I've got a physics test in a couple of days and I have some questions:1. In a calculation, if the acceleration is in m/s², I presume the speed also has to be in m/s and not in km/h ? 2. So with this graph (v with t), I have to find the total...
12. ### 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...
13. ### Linear motion question -- Drops falling from a dripping faucet

Hello, I am a new member looking for the answer to a question I recently had on an exam. I will not know if I got it right for up to 6 weeks so am curious. Question is: A faucet drips water at 5 drops per second. calculate the distance in metres between the first and second drop after the first...
14. ### Linear Motion Formulas for an Inclined Plane

Homework Statement The initial speed of a ball up an inclined plane is 3 m/s upwards. The ball reaches its highest point after 1.2 seconds. a) find the acceleration. b) how far has the ball gotten during this time? c) how far has the ball rolled after 0.4 s and after 2.4 seconds? Homework...
15. ### Ways to Spin a Flywheel using linear motion

I am to try to find simple way to spin a spinning flywheel. What linear motion device acting on the outside edge of a spinning flywheel can be used to increase the speed of the flywheel. Need to use a repeating pattern such as pushing your hand down over and over on the edge of the wheel to...
16. M

### Solving Linear Motion Problems: Initial Speed, Time, and Height

Homework Statement "A ball thrown straight up with an initial speed of 30/m/s. (a) Show the time it takes to reach its trajectory will be 3m/s (b) Show that it will reach a height of 45m" Homework Equations h=ut+1/2g^2 1/2gt^2 The Attempt at a Solution Part a of the question I am fine with...
17. ### How to understand linear momentum?

I understand for linear momentum the measure of the dificulty to take a body to the rest. But when I do the next exercises, I find that it requires less force for one body compared to the other with same linear momentum. Can someone explain me what to understand in an intuitive way what to...
18. C

### Acceleration and velocity: Car and train problem

Homework Statement A train has a length of 118 m and starts from rest with a constant acceleration at time t = 0 s. At this instant, a car just reaches the end of the train. The car is moving with a constant velocity. At a time t = 14.0 s, the car just reaches the front of the train...
19. ### Rotary to linear motion using a crank

Hello guys, since linear motors are too expensive I decided to buy a rotational motor and use some gears and a crank mechanism to get enough torque and translate rotation into linear motion. I need to meet a certain force on the shaft though. The question is how do I calculate the resulting...
20. ### Best way of turning rotational motion into linear motion?

Hello everyone, I am not an engineer, so I apologize if this is a relatively simple question. What's the best way to turn rotational motion into linear motion under the following circumstances? 1. Rotational motion is driven by a vertical bolt. 2. When turned, the bolt will extend a bar...
21. ### Particle dynamics applied to geometrically parametric line

I have an odd, yet intriguing question. I want to describe a particle that is constrained to move along a straight line in the x direction. The location of the particle can be described with theoretically infinite parametric parameters, d, along the line. For example: R = [d 0 0]T R = [d2 0 0]T...
22. ### Collision involving angular and linear motion

Homework Statement a small 0.199 kg block slides down a frictionless surface through height h = 0.608 m and then sticks to a uniform vertical rod of mass M = 0.398 kg and length d = 2.23 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ. point O is at the end...
23. ### Linear Motion and Free Fall: Solving Projectile Motion Problems

I. Free Fall Motion A mass m = 544 g is thrown straight up with an initial speed of 3.50 m/s from a height of h = 2.50 m Neglecting a drag force, determine: 1. The acceleration of the object while it moves up. 2. The acceleration of the object at the highest point. 3. The maximum height...
24. ### Hey guys, I'm just here to see if anyone can help me

I've just started my accelerated physics course and am looking for a tutor-like mentor. I am working on my pre-med degree, while working in the medical field. 18 units this semester doesn't leave me much time to meet with tutors. Let me know if I can bug any of you with my Physics I homework...
25. ### Linear Motion Question: Object thrown vertically

Homework Statement An object is thrown upwards vertically with an initial speed of a and an initial height of h. It travels for t seconds until it hits the ground with a speed of b. If a was 0.5a, what would the hang time be in terms of t? Homework Equations xf=xo+vot+.5(-10)t^2 vf=vo+(-10)t...
26. ### Linear Motion Question: Ball thrown in the air

A ball is thrown upwards from a building of height 2x with an initial velocity of v1. The velocity when it hits the ground is -v2. What is the height of the ball when it is at maximum speed? Since it is at its max speed when it hits the ground, would the answer just be 0x?
27. ### Can spinning motion be converted into linear motion?

Hi, I've been working on a school project which involves investigating the momentum before and after a collision between two steel balls. E.g. we have Ball A (moving) and Ball B (stationary), which are of identical mass. Ball A collides into Ball B. What we have observed is that Ball B then...
28. ### Constraints for Linkage system

Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...
29. ### How the solenoid gets the linear motion when the current is passed in the coil?

The Solenoids which are used for pneumatic controller uses the solenoid as a switch to control the value opening and closing. This is done by passing current to through the coil which produces the magnetic field . But i would like to know how the generated magnetic field will move the solenoid rod?
30. ### I have a problem with variable forces

Homework Statement A force F has components F sub x = axy-by^2, F sub y= -axy+bx^2 where a= 2N/m^2 & b=4N/m^2 Calculate the work done on an object of mass 4kg if it is moved on a closed path from (x,y) values of (0,1) to (4,1), to (4,3) to (0,3) and back to (0,1). all coordinates are in metres...
31. ### Electric Motor for Linear Motion w/Steering Horn

I want an electric motor that works a bit like a servo motor with a steering horn on it, like so: http://www.buggy-sport.info/index.php/gallery/image?view=image&format=raw&type=img&id=7191 But it needs two specific properties: - it creates a controllable amount of force along a given axis...
32. ### What is the acceleration of Steve Prefontaine during his 10-km race?

In April 1974, Steve Prefontaine completed a 10.0-km race in a time of 27 min, 43.6 s. Suppose “Pre” was at the 9.00-km mark at a time of 25.0 min even. If he accelerates for 60.0 s and maintains the increased speed for the duration of the race, calculate the acceleration that he had. Assume his...
33. ### Calculating Vertical Motion: Am I on the Right Track?

Wondering if I am on the right track with below question A body is projected vertically upwards from ground level with an initial velocity of 400m/s. determine; (a) Time to reach the ground (b) Velocity at a point 1.8km above the ground (c) Time to reach a vertical height of 2.5km. (a)...
34. ### What Are the Equations for Equilibrium and Motion in Physics Problems?

Homework Statement Just in case my interpretation of the diagram does not give a clear representation, here is a link to all of the questions. http://imgur.com/a/jsv9e The question begins by asking me to state the necessary conditions for a body to be in a state of equilibrium. It is a...
35. ### Can You Solve These Challenging Linear Motion Problems?

Homework Statement 1) Harry Hopeless averages 40km/h for the first half of his car trip. How fast should he drive on the remaining half of the trip to have an average speed of 80km/h for his trip? 2) You drive to the city at an average speed of 40km/h and return at an average speed of...
36. ### Linear motion in central field

Homework Statement I have two masses of finite width, m_1 and m_2. The force is Newton's gravity, so U = k/r. I want to work out their relevant equations of motions r_1(t) and r_2(t) as they start off from rest and collide. I don't want to consider any rotational motion. Homework...
37. ### Linear motion converted into rotatory motion problem

Homework Statement In a ballistic pendulum an object of mass m is fired with an initial speed v_0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular...
38. ### Rotational Motion to Linear Motion

This is a question for a rather odd purpose. I came across a working LEGO model of a Russian tank and I'm trying to model it using CAD software. It has a motorized system to elevate and lower the main cannon. This is where putting it into words might get weird: It uses a small motor which...
39. ### What Is the Acceleration of a Thrown Ball at Its Peak?

Homework Statement Problem A: A ball is thrown upwards and returns to the throwers hand. Air resistance is ignored and the upwards direction is taken as positive. Circle the correct values for the acceleration of the ball: Going up : g / 0 / -g At max height: g / 0 / -g Going down: g...
40. ### Linear motion: a runner with two accelerations: 1 constant other not

Homework Statement Problem 3.7 Suppose that motion studies of a runner show that the maximum speed he can maintain for a period of about 10 s is 12 m/s. If in a 100-m dash this runner accelerates with constant acceleration until he reaches this maximum speed and then maintains this speed...
41. ### Apparent paradox with angular and linear motion

A friend raised an observation which I thought would be easy to explain. But it seem I have a gap in my physics knowledge... An object (rigidbody) is stationary in zero gravity empty space. In the first situation we apply an impulse to its COG and its linear momentum changes, and no angular...
42. ### Impulse momentum method for linear motion

Homework Statement I was told by a friend that M1+I1-2=M2 is actually FT=mVf-mVi. So using FT=mVf-mVi to solve the following question... The Attempt at a Solution FT=mVf-mVi (F)(0.15)=800(0)-800(5000/3.6) F=-7407.4N Ans is 7407.4N positive. Can I ask did I get my sign wrong?
43. ### How can I create a mechanism for precise linear motion in two planes?

Hey guys, I'm brainstorming some ideas for a mechanism that will be able to move an object in the vertical plane up and down, as well as left to right. Essentially I'm looking at controlling the X and Y coordinates of this moving mass. I want to be able to move in the vertical plane, lock it...
44. ### Problems with acceleration results established from equations of linear motion

I have 3 separate cases of an object decelerating at different rates. The aim is to find the acceleration for each case. Case 1 Initial velocity: 1.663m/s Displacement: 0.12m Time: 0.139s Case 2 Initial velocity: 1.663m/s Displacement: 0.12m Time: 0.155s Case 3 Initial Velocity: 1.663m/s...
45. ### Work Energy Method for Linear Motion

Homework Statement From my textbook there is a note that says " A reference datum must always be define in order to obtain the height h. I don't quite understand what is it trying to tell me. I already had define my datum 1 as position 1 and datum 2 as position 2. On my 2nd diagram , I...
46. ### Help creating constant-speed linear motion

I want to move a plate at a constant speed in a straight line, and to do so in as efficient a way as possible with high torque involved. What would be a good method to accomplish this? The problem is that both torque and efficiency are very important.
47. ### Linear motion with variable forces

Homework Statement A racing car of mass 20000kg accelerates with a driving force of 480(t-10)^2 Newtons until it reaches its maximum speed after 10 seconds. Find its maximum speed, and the distance it travels in reaching this speed. The Attempt at a Solution Again, I can't seem to...
48. ### Linear motion with variable forces

Homework Statement A car of mass 1200kg is at rest on a level road. Two people push it, producing a total force given by (240-12t) Newtons, where t is the time in seconds, until this becomes zero after 20 seconds. How fast is the car then moving, and how far does it move while it is being...
49. ### Understanding Linear Motion: Solving for Travel and Remaining Distance

http://store2.up-00.com/May12/Ueu86896.jpg someone here told me that travel distance is = vs = 30 m now remaining is 60 - 30 = 30 m now my questions is ... to solve this Q we use which distance is travel distance or remaining distance
50. ### Questions in linear motion and rotating motion

Hi please I want from you check my answer http://store2.up-00.com/May12/Ueu86896.jpg http://store2.up-00.com/May12/fkl86896.jpg