What is Rectilinear motion: Definition and 36 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


{\displaystyle x}
, which varies with


{\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. N

    How to show that P moves with a constant speed u

    For particle Q: The resultant force on particle Q would be zero since it is at rest. Thus$$ T - Mg = 0$$ which gives $$T = Mg$$ For particle P: This is where I am struggling. I can't seem to write out the polar equations of motion. I have to show that $$u^2 = (Mgb)/m$$ I know that $$\vec a =...
  2. Terrycho

    Rectilinear motion, not uniform accleration

    The photo above is the problem I'm struggling now and the photo below is what I have done so far. By differentiating and integrating the given equation, which is F=-b exp(αv), I tried to express v(t) or a(t) as a function related to t, which is time. But the more I did, the more complicated...
  3. L

    I Having a hard time remembering what this equation is

    Ok, so it has been about 4 years since i have had physics for scientists and engineers. I am a full time mechanical and areospace student. I just started dynamics class and right off the bat, i ran into an equation that i am not sure how to infer. It is from our rectilinear example: d^2x/dt^2 =...
  4. Alexanddros81

    Pytels Dynamics 12.40: The rocket sled is propelled....

    Homework Statement The 13-kN rocket sled is propelled along a straight test track. The rocket engine fires for 4 seconds, producing a propulsive force of F=5.3kN, and then shuts down. Assuming that the sled starts from rest and that the coefficient of kinetic friction is 0.05, determine the...
  5. N

    MHB Rectilinear motion problem

    A particle moves along the x-axis according to the equation s(t) = 1/3t^3 -t^2 -8t +12, where s is the directed distance (in meters) of the particle from the origin at time t (in seconds). Find a. the directed distance of the particle from the origin, its velocity and acceleration at the...
  6. P

    A question about Rectilinear motion

    Homework Statement Q: If a particle moving along a straight line under uniform acceleration covers successive equal distances ( S each) in time intervals t1, t2 and t3 respectively, then the expression for average speed of particle in covering the given distance of 3S is: Options: A) (S/t1)...
  7. Abel Cavaşi

    The informational paradox of rectilinear motion

    If the torsion of the straight line is undefined what happens with the information about the torsion? It is known (https://en.wikipedia.org/wiki/Quantum_no-deleting_theorem, http://van.physics.illinois.edu/qa/listing.php?id=24045) that the information conserved in a system can be nor created...
  8. H

    Rectilinear motion of two attracting masses

    Homework Statement Consider two masses of variable magnitude (M m) that are separated by a distance ( r ). Both masses are free to move. Calculate dr/dt. Homework Equations (See below) The Attempt at a Solution F = GMm / r2 a = Gm / r2 let k = Gm da/dr = -2kr-3 dr/da = (-2k)-1 r3 dr/da *...
  9. D

    Does quantum gravity argue that space is not singularly....

    Does quantum gravity argue that space is not singularly occupied by rectilinear motion?I am reading a general relativity intro sort of thing and this inquiry popped up in my mind. The text was explicating space being occupied by only rectilinear motion and I wondered if quantum gravity could be...
  10. F

    Problem for the Geniuses

    A scientist is performing an experiment on an up-the-floor escalator in a mall. The scientist ran up the escalator and took 50 steps to reach the upper boom. Then, he ran back down the same escalator and took 125 steps to reach back the lower boom. The pace of the scientist going down is five...
  11. M

    Calculate Distance Traveled: Car Acceleration from 30 km/hr to 88 km/hr in 7s

    A car moving at 30 km/hr accelerates for 7.0 s. after which its velocity is 88 km/hr. How far does the car travel while its accelerating? Given: Initial Velocity : 30 km/hr Final Velocity : 88 km/hr Time : 7 seconds Acceleration: ? Distance: ? correct me if I'm...
  12. L

    Piecewise Rectilinear Motion Integration

    Homework Statement Suppose that a particle moves along a line so that its velocity v at time t is given by 5t, if 0≤t<1 (6(t)^(1/2))-(1/t), if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the particle is 4 cm from its starting position...
  13. M

    Can't seem to integrate this rectilinear motion equation.

    Hi, so I have a question where it asks me to find the distance between t = 0 and t = 60 for the equation v = 1/6(t(60 - t)). First I had to find the values of t which the object moving was stationary, that was simple enough. (It's been around a month and a half since I did rectilinear motion)...
  14. M

    Rectilinear Motion Take-Home Exam - DEAD END

    Hi everyone. I'm in crisis mode over this take-home exam I have due in 12 hours. I've posted the 4 problems I'm stuck on and ANY help would be a life-saver. I can get all of them setup, but am completely clueless as to how to actually execute them. I have a few questions in specific...
  15. X

    Rectilinear Motion: Solving for t=0 Velocity

    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=5 seconds, the acceleration of Q is 12t ft/s^2 to the left. If after 2 more seconds point Q is 13...
  16. X

    Rectilinear motion (displacement, position) calculus

    Homework Statement A particle has a linearly varying rectilinear acceleration of a=x''i=(12t)i m/s^2. Two observations of the particle's motion are made: Its velocity at t = 1s is x'i=2i m/s, and its position at t= 2s is given bt xi=3i m. (a) Find the displacement of the particle at t=5s...
  17. X

    Kinematics of a point in rectilinear motion

    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...
  18. @

    Solving Rectilinear Motion: Find Velocity & Position

    Homework Statement Find velocity and position as functions of time t for a particle of mass m, which starts from rest at x=t=0, subject to the following force functions. a) F=Fosin(ct) Homework Equations F=ma The Attempt at a Solution a) a=Fosin(ct)/m dv/dt =...
  19. J

    Rectilinear motion of a particle

    A particle of mass m moves without friction subject to a force F(x) = −kx + \frac{kx3}{A2}, where k and A are positive constants. It is projected from x = 0 to the positive x direction with initial velocity v0 = A\sqrt{\frac{k}{2m}}. Find: (a) the potential energy V (x), (b) the kinetic...
  20. BloodyFrozen

    Solving Rectilinear Motion Equations - Deriving at^2+v+h

    I can't remember how to derive this equation... x(fluxion) a=acceleration x=a From that, how do we get-> at^2+v+h I think it had to do with integration, but I can't seem to get it to match the above.
  21. L

    Kinematics: Rectilinear Motion (calculus)

    Hello, first post here. I've used these forums as reference for quite some time, just never actually made an account until now. I'm working through the textbook for my upcoming Intro to Dynamics class and I am having trouble figuring out this problem. It seems like it should be pretty...
  22. X

    Kinetmatics of rectilinear motion

    Homework Statement A point P starts from rest and accelerates uniformly (meaning x'' = constant) to a speed of 88 ft/sec after traveling 120 ft. Find the acceleration of P. Homework Equations x=position v=velocity=dx/dt a=acceleration=dv/dt The Attempt at a Solution The...
  23. D

    Kinematics of rectilinear motion - multiple displacements

    Homework Statement A cheetah is estimated to be able to run at a maximum speed of 100km.h^1 whilst and antelope can run at a maximum speed of 65km.h^-1. A cheetah at rest sees an antelope at rest and starts running towards it. The antelope immediately starts running away. Both cheetah and...
  24. 0

    Rectilinear Motion (Object dropped 500m, will it burst?)

    Homework Statement An object is dropped from a height 500 m above the ground. This object is designed to withstand an impact velocity of 100 m/s. Will it burst? Homework Equations gravitational force: 9.8 m/s The Attempt at a Solution s(t) = 500 m a(t) = 9.8 m/s v(t) = ...
  25. L

    Motion along a line (Rectilinear Motion) Help

    Alright, so I attached pictures of the problem from my textbook. I thought it would make it easier for you to help me. I am having trouble picturing the velocity, acceleration and speed. If someone could help me through a, b, c, and d, I would love the help. Thanks
  26. A

    Rectilinear Motion Problem

    Homework Statement A block of wood is projected up an inclined plane with initial speed v0. If the inclination of the plane is 300 and the coefficent of sliding friction uk=0.1, find the total time for the block to return to the point of projection. Homework Equations fA=ukN N=mgcosθ...
  27. F

    Rectilinear Motion with Constant Acceleration

    Homework Statement (1) If you measure the acceleration of the falling mass to be 7.2 m/s^2, should you be concerned that you somehow made a mistake? What if you found the acceleration to be 11.5 m/s^2? For this question, a falling mass is attached to a piece of paper, which is subsequently...
  28. A

    Mechanics - Rectilinear Motion

    Homework Statement A train travels between two stations 4.5km apart. If the maximum acceleration is 3m/s2 and the greatest deceleration is 4.5m/s2, find the shortest time between the two stations if the maximum speed allowed is 100km/hr. Max Acc. = 3ms-2 Max Dec. = 4.5ms-2 Max speed =...
  29. A

    Rectilinear Motion of Particle

    Homework Statement 3. The acceleration of a particle is directly proportional to the time t. At t=0, the velocity of a particle = -12 m/s. Knowing that v=0 and x = 15 when t=4s, write the equation of the motion. Here is my solution, could Somebody check it? Text is in Polish, sorry...
  30. E

    AP Calc Q: Find Time When Object at x=10/3

    Hey guys I need some help with one of my AP Calc question. My luck is that it will be very simple. Thanks for your help Homework Statement The velocity of an object, starting at the origin, and moving along the x-axis is given by V(t)=(t-1)(t+1)^1/2. Find the time when the object will...
  31. Saladsamurai

    Solving Rectilinear Motion: Find Car Acceleration at t=4s

    [SOLVED] Rectilinear Motion Homework Statement A car starts from rest and moves along a straight line with acceleration a=3s^{-1/3}m/s^2 where s in meters. Determine the cars acceleration at t =4 seconds. I know that I am given acceleration as a function of position. I know that by the...
  32. T

    Basic Rectilinear Motion Question

    I am confuse with the following Kinematics problem PROBLEM A helicopter accelerates uniformly upward at 1m/s^2 to a height of 300 m. Determine the time required for this motion. SOLUTION s = 300 m v0 = 0 a = 1 m/s^2 v = v2 s = (v0) (t) + (1/2) (a) (t^2) 300 m = 0 + (1/2)...
  33. S

    Rectilinear Motion Help please

    Hi, I recently stumbled across your forums whilst trying to find help for my homework. I have managed to do all the questions on the homework except these 2, and i cannot seem to get the right answers to them. This is because they both miss one piece of data and i would normally use the suvat...
  34. C

    Momentum-impulse vs. rectilinear motion equations

    Here we are again...We have apully system as seen on page 1 of the attachment. I tried using the rectilinear motion equations, assuming a=constant, but the book's solution used the momentum-impulse equations and got a different answer. I don't understand why my approach is incorrect... Thanks.
  35. M

    Transitions from Rest State to Rectilinear Motion: Infinite Jerk?

    Anyone- From long ago IIRC a body that transitions from a rest state to a rectilinear moving state undergoes nearly infinite jerk (change in 'a'). On the one hand, my memory is reinforced by the idea that not all functions have infinitely many derivatives... But on the other hand, I may not...