# What is Accelerated motion: Definition and 67 Discussions

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time.
Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:

the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force;
that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.The SI unit for acceleration is metre per second squared (m⋅s−2,

m

s

2

{\displaystyle {\tfrac {\operatorname {m} }{\operatorname {s} ^{2}}}}
).
For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during circular motions) acceleration, the reaction to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or orthogonal during circular motions) acceleration, the reaction to which the passengers experience as a centrifugal force. If the speed of the vehicle decreases, this is an acceleration in the opposite direction and mathematically a negative, sometimes called deceleration, and passengers experience the reaction to deceleration as an inertial force pushing them forward. Such negative accelerations are often achieved by retrorocket burning in spacecraft. Both acceleration and deceleration are treated the same, they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in reference to the vehicle.

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1. ### I Invariant definition of acceleration in Newtonian physics vs proper acceleration in GR

Does it exist an invariant way to define acceleration in Newton physics like the proper acceleration in GR ? In Newton physics if an accelerometer attached to an object reads 0 it does not mean it is actually not accelerating (since gravity is a force). To define inertial motion the concept of...
2. ### Average velocity ##\bar{v}## for a uniformly accelerating particle

Statement of the problem : Let me copy and paste the problem from the text. Please note it's part (i) that I am seeking to answer. I know the answer to part (ii). Solution : To show where my error appears, I take the time(s) to be ##t_f## and ##t_i##, whereby the given time interval ##t =...
3. ### I Calculate Length Contraction for Accelerated Motion to Proxima Centauri

Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2. The ship is accelerating the first half of the trajectory and decelerating the second half. I calculated the velocity profile from the Earth reference: The travel time on...
4. ### B Metric Line Element Use: Do's & Don'ts for Accelerated Dummies?

From Wikipedia article about Hyperbolic motion, I have the following coordinate equations of motion for Bob in his accelerated frame: ##t(T)=\frac{c}{g} \cdot \ln{(\sqrt{1+(\frac{g \cdot T}{c})^2}+\frac{g \cdot T}{c})} \quad (1)## ##x(T)=\frac{c^2}{g} \cdot (\sqrt{1+(\frac{g \cdot T}{c})^2}-1)...
5. ### I Twin Paradox with accelerated Motion

Alice rests at ##X=L+1## in the inertial frame (T, X). Bob is at rest in the Rindler frame (t, x) at ##x=1## and has the proper acceleration ##\alpha=1##. In the rest frame of Alice, Bob moves from event ##E_1=(-T_2, L+1)## over the distance of ##L## in negative X-direction to event ##(0, 1)##...
6. ### I Twin paradox for (accelerated) dummies?

Applying the Lorentz transformation to velocity and acceleration, we can easily obtain that Aγ3 = α, where A is the acceleration measured by the stationary observer and α is the proper acceleration of the relative moving object. From this point, the equations for a constant accelerated motion...
7. ### I When and how can I apply Born rigidity condition?

Hello, I try to better understand how and when I can apply the Born rigidity condition. So, for the following example: We've two space probes (Pa and Pb), that travel at an exact equal and same proper acceleration. At a given time tb0 in Pb, and as measured by Pb, the distance is Lba0 (it's...

Thinking about Bell's string paradox , I understand that if both spaceships maintain the same and constant proper acceleration, the string breaks because of the non-simultaneity of the acceleration effects at both ends of the string. But I want to introduce and consider a slight and subtle...
9. ### I Why are acceleration, jerk, etc not relative, just like velocity?

I've been thinking about this for a while, and thought it would be nice if someone could guide me to an answer. In Newtonian mechanics, an inertial frame is coordinate system that's able to make measurements with respect to some imaginary axes attached to it. It's a well known fact that velocity...
10. ### I Comparing Clock Rates in Accelerated vs Constant Velocity Frames

@PeroK sent me here based on a discussion starting at https://www.physicsforums.com/threads/some-ideas-on-interstellar-space-travel.1006562/post-6550265. Summary: Someone claimed that an accelerated observer's clock (observer at 1g from Earth to halfway to Alpha Centauri, then -1g the rest of...

12. ### Finding height in uniformly accelerated motion

First of all I have found the time taken by the first object to hit the ground back: ##\Delta t=2(\frac{v}{a})##. Then, by subtracting 2 seconds to this quantity, I get the time in which the second object has accelerated in free fall, with terminal velocity ##v=at##. Now, I find the distance...
13. ### Uniformly accelerated motion issue

I went quite confidently on this one, at least at the beginning... I found the instant velocity on the 3rd second(v1=12.2m/1s) and the one on the 4th(v2=14.4m/1s), and subsequently the acceleration(a=2.2/1m/s*s). Since the acceleration is constant, using the law "v=v0+aΔt", I have found v0 which...
14. ### A Proving Free-Fall in Rindler Spacetime is Finite

Okay, so, while discussing Rindler space with my professor, I was asked to prove that for a free-falling observer, proper time for passing through the Rindler horizon is finite. That is at least how the question is phrased. So, the professor obviously assumes that it is clear and trivial to me...
15. ### Calculate velocity of stopping car

Homework Statement A car moving at 20m/s starts decelerating, travels distance d, and stops. Find the car’s velocity at distance d/2. Homework EquationsThe Attempt at a Solution my brain is fried. I feel like I’m missing something obvious but I just don’t get it.
16. ### Projectile Motion and acceleration of particle

Homework Statement If a particle moves in X-Y plane with acceleration non zero in X and Y , the particle will not move in a parabolic path True or False ? Homework Equations X = UxT + 1/2(Ax)T^2 Y= UyT + 1/2 (Ay)T^2The Attempt at a Solution The equation of trajectory that i came up with...
17. A

### Solving for Constant Centripetal Acceleration: Understanding Spiral Motion

Assume an object accelerating at a certain value dV/dt. If this object was traveling in a circular motion the centripetal force would increase as the object moves faster. To maintain centripetal acceleration constant while the object is accelerating (in its forward motion dV/dt) I think it...
18. ### What Is the Correct Way to Calculate Average Force in a Jumping Scenario?

Homework Statement A person jumps from the roof of a house 4.2-mhigh. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.66 m . If the mass of his torso (excluding legs) is 43 kg , find the magnitude of the average force exerted...
19. ### Direction of vector acceleration in circular motion

There is a problem in my Physics textbook which says: Homework Statement "A car runs counter-clockwise in a circular lane of 1 km of diameter, going through the south extreme at 60 km/h on the instant t = 0. From that point onwards, the driver accelerates the car uniformely, reaching 240 km/h...
20. ### I Determine P(t)=(Px(t),Py(t)) given (x0,y0) and v(x,y,t).

Dear all, I'm a bit confused about a 2D problem which I thought had a simple solution... I don't know if I'm correct, so: I have a 2D space, and time. I know the velocity field v(x,y,t). I would like to know where the particle which start at the position x0,y0 at an istant t0 is at a certain...
21. ### Questions about uniformly accelerated motion under gravity

I am not able to understand that why when a body is traveling against the gravity, there will be a point somewhere (which will be known as the maximum point where it will change its path, towards the ground) where the body's velocity become 0 m/s. Then it returns to the ground. So my doubt is...
22. ### Uniformly accelerated motion under gravity

Uniformly accelerated motion under gravity:- I have been taught that when a body accelerates, it travels on ratio of 1:3:5... so on. I have also been taught that at the last second, anybody in the world will travel with the velocity of 5 m/s. Why is that so? Why I should believe on some axiom.
23. ### Equation of accelerated motion in GR

Hello forum members, I decided to post in the homework section because my question seems very basic to me. Still I'm getting stuck with it and would appreciate any help. Homework Statement I am teaching myself foundations of GR with the goal of simulating numerically some motion in flat and...
24. ### Strange acceleration graph during a jump

Hi! I have just performed some experiments with my phones accelerometer, and plotted the acceleration as a function of time from the raw data. The experiments I did was: jumping down from a chair jumping from the floor and up let the device fall toward a bed When I analyze the graphs, I think...
25. ### 1D-kinematics with constant acceleration

1. A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time the figure...
26. ### What is the average force on the wall?

Homework Statement A ball hits the wall in a normal direction with v=10m/s. After the hit which lasted 0.2 Seconds, it turned in the same direction with v=10m/S. Knowing that its mass is 0.5 kg, find the average force that hit the wall. Homework Equations F=m*a, a= (v-v0)/t The Attempt at a...
27. ### Find Magnitude & Direction for acceleration

Homework Statement Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A? Homework Equations a_A = a_B + a_A/B x_A = x_B + x_A/B y_A = y_B + y_A/B The Attempt at a Solution x & y components: -4cos(20) =...
28. ### Find Magnitude & Direction for acceleration:

Homework Statement : Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A?[/B] Homework Equations a_A = a_B + a_A/B[/B]The Attempt at a Solution a_A = 4 +4 = 8 m/s2 <-- 8*cos(20) = 7.52 (x-component)...
29. ### Relativistic Uniform Accelerated Motion

Homework Statement Hi I am supposed to calculate the distance traveled by a particle that is uniformly accelerated with acceleration equal to the Earth's gravity (i.e. a=9.81m/s^2) after 1, 10 and 100 years proper time. Homework Equations We derived in class the four vector which describes the...
30. ### Calculating the velocity decrease going up an incline

I know there are many factors that go into this. But in general how would one go about calculating the angular velocity for a car going up an incline. What I want to know in particular is if a car say is driving at a consistent speed of 60mph on an even plane and then hits an incline up wards at...
31. ### Velocity of Accelerated Observer in SR: Understanding the Paradox

Hey, I have a question regarding accelerated motion in special relativity. Suppose an observer has a constant proper acceleration α, his velocity in an inertial frame of a distant observer will then be given v = c tanh(ατ/c), where τ is the proper time of the accelerated observer. Since every...
32. ### Equations for Accelerated Motion (Two problems)

Homework Statement A sailboat in a race is moving at 2.5 m/s when it crosses the starting line. It begins to accelerate at 1.1 m/s^2. How long does is take to travel 80m past the starting line? Homework Equations vavg=(vfinal+vinitial)/2 t=x/vavg v^2=vinital+2aΔx The Attempt at a...
33. ### Equations for Accelerated Motion 4

Homework Statement A motorcycle traveling at 30 m/s comes to a stop over a distance of 150 m. What was the motorcycle's acceleration? Homework Equations v^2=vinitial+2aΔx The Attempt at a Solution I tried plugging in what I know. 0=900+2a*150 m Then I divided 150 m and 900 by...
34. ### Equations for Accelerated Motion 3

Homework Statement A drag racer has an acceleration of 3g. What distance is needed for the car to reach a speed of 320 mi./h (143 m/s)? Homework Equations v^2=vo^2+2aΔx The Attempt at a Solution I decided to use m/s to make it easier. 143 m/s^2=0+2(9.8*3)Δx 20449=58.8Δx Δx≈347.7 m...
35. ### Equations for Accelerated Motion Problem 2

Homework Statement A car traveling at 60 mi/h stops in 6 seconds. How far does it travel during this time? Homework Equations a=Δv/Δt x=xinitial+vinitialt+1/2(a)t^2 The Attempt at a Solution First I changed units into the standard ones: 60 mi/h *1609.34 m/1 mi * 1 h/3600 s =...
36. ### Equations for Accelerated Motion Problem

Homework Statement Starting from rest, a car accelerates for 8 seconds with a constat acceleration. During this time it travels 121 meters. Find its velocity at the end of the 8 seconds. Homework Equations a=(2x)t^2 Vavg=(Vinital+Vfinal)/2 The Attempt at a Solution First, I found...
37. ### Accelerated Motion in [2]- initial speed and launch angle

Homework Statement The range of a projectile is 483m, and it reached a maximum height of 65m. What were the initial speed and launch angle of the projectile? Assume the start and finish heights are equal. Homework Equations The Attempt at a Solution I just need a push in the...
38. ### Trouble with Uniformly Accelerated Motion problem

So I acquired an old Physics textbook (Gioncoli Physics 2nd Edition) out of which I am attempting to learn classical mechanics from. It's in Algebra and not Calculus so I thought I could do it since I just completed Advanced Algebra 2 w/ Trigonometry this year. The first chapter is on Kinematics...
39. ### How Do You Calculate Deceleration from Average Velocity?

Homework Statement A car decelerates uniformly and comes to a stop after 10 s. The car's average velocity during deceleration was 50 km/h. What was the car's acceleration while slowing to a stop? {Since the acceleration is UNIFORM (constant), use vavg = (v0 + v)/2... } Homework Equations The...
40. ### Uniform accelerated motion question

Homework Statement A sprinter runs a race with constant acceleration throughout. During the race he passes four posts A, B, C, D in a straight line such that |AB| = |BC| = |CD| = 20m. If the sprinter takes 5 seconds to go from A to B and 3 seconds to go from B to C, find out how long, the the...
41. ### Uniformly Accelerated Motion: A Puzzling Problem?

The problem statement: A particle travels along the x-axis with uniformly accelerated motion. At times t and s its position is x and y, respectively. Show that its acceleration is a = 2(yt-xs)/ts(s-t). The attempt at a solution: I could be wrong, but it seems to me this problem is...
42. ### Rearranging equations of accelerated motion

Homework Statement theres two questions actually. 1) a boat increases its speed from 5.0 m/s to 7.5 m/s over a distance of 50.0m. what it the boat's acceleration? 2) within 4.0s of liftoff, a spacecraft that is uniformly accelerating straight upward from rest reaches an altitude of...
43. ### Backreaction of accelerated motion on spacetime curvature

Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature? Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.
44. ### Doppler shift for accelerated motion

I was talking to one of my friends the other day about doppler effect and we went into the discussion of accelerating object and doppler effect. we both agreed that the frequency shift would vary in time. then we argued about the frequency shift for different observers and here is were it got...
45. ### Comparing Constant Velocity and Accelerated Motion

I want to know the comparison between a body in motion with constant velocity and accelerated motion? Like a body when it is motion with constant velocity its velocity is constant(v =constant) and acceleration (a=0)...? and when a body is in accelerated motion its velocity will be constant(v...
46. ### What is the effect of gravity on a thrown stone?

A stone is thrown straight upward with a speed of 20m/s. It is caught on its way down at a point 5m above where it was thrown. Find (a) How fast was it going when it was caught? (b) How long did the trip take? Let us take up as positive. Then, for the trip that lasts from the instant after...
47. ### Uniformly Accelerated Motion for Short Distances

Why don't these equations (and the rest in the set) work over long distances? Vf= V0 + at D= (1/2)(V0 + Vf)t D= (V0)(t) + (1/2)(a)(t2) etc...
48. ### How Do You Calculate the Distance Traveled in the Last Second of Acceleration?

Homework Statement A plane starts from rest and accelerates in a straight line along the ground before takeoff. It moves 600m in 12s. Find a) acceleration, b) speed at the end of 12s, c) the distance moved during the twelfth second. Homework Equations d = vot + 1/2at^2 v = vot + at...
49. ### Equation of uniformly accelerated motion

Homework Statement A ball is thrown vertically upwards at 16ms^-1. What is the velocity after 2 seconds (acceleration is 9.8 m/s/s) Homework Equations v = u+at V=velocity u= Initial speed a=acceleration down to earth t=Time The Attempt at a Solution I don't quite understand it.
50. ### Help on this accelerated motion problem please

Homework Statement A stone is dropped from the roof of a high building. A second stone is dropped 1.31 s later. How far apart are the stones when the second stone has reached a speed of 19.3 m/s? Homework Equations well... stone 1 V0 = 0m/s vf = unknown t = unknown a = -9.8m/s/s...