What is Acceleration: Definition and 1000 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. amandela

    Rolling Motion (Stone Gets Stuck in a Tire Going Forward)

    So I thought the stone would initially experience acceleration in the backward (leftward) direction then continually accelerate in the inward direction of the tire (i.e. upward then rightward then downward then leftward, etc.) as the tire moves forward. But the answer is immediately upward...
  2. MatinSAR

    If a rope is in free fall, does tension force act on it or not?

    This is the question. To this point everything is clear. I have problem with following part: The authors claim that each part of the remaining rope is under constant acceleration. So it is in free fall and only gravitional force acts on it. If we release a rope like above, before it hits the...
  3. I

    POWER - different approach, different results

    Basically, I tried to find the solution by calculating P=Fs/t, where F= 2250 and s is the distance traveled in the 12th second and that result differs from the result I get when I calculate the power using P=Fv. ##F=ma=1500*1.5=2250N## ##s_{12}-s_{11}=...
  4. amandela

    Work Done and Acceleration (Mistaken Answers?)

    So for Q1, I answered down (towards Earth) but the solution says there is no acceleration there. For Q2, I answered mgh, but the solution says it's mgh/t, which is power, right? I just want to make sure I'm not super confused. Thank you.
  5. amandela

    Instantaneous Acceleration Given Equation for Velocity

    This is from an old exam. The velocity of a particle moving along a straight line is v = 4 + 0.5 t. What is the instantaneous acceleration at t=2? The solution is supposedly 2 because a = dv/dt = t. But I thought dv/dt here would be 0.5. What am I missing? Thanks.
  6. P

    I Coriolis effect and the acceleration experienced in a rotating frame

    Is the reason behind coriolis acceleration is that as you move far from the centre of a rotating frame the tangential velocity increases?
  7. chwala

    Calculate acceleration and speed of block

    Pretty straight forward, ...reason of posting is to check why i am having a negative value for ##a##. From my study, i know that ##R(||)## to plane ##F - 40 \cos \dfrac{π}{3} = 4a## ##a = -5 m/s^2## or can i as well have the equation ( friction and tension are at equilibrium) as, ##40...
  8. S

    Having a hard time learning Newton's 2nd law

    I'm taking college physics without calculus this semester and it's been quite the challenge to say the least. We recently covered free body diagrams and while I understand the different vectors in the FBD, making calculations is killing me. Specifically Newton's 2nd law. The problems range...
  9. SSJBLOOD

    Find the coefficient of friction and acceleration with masses given

    I tried to use the energy route but the acceleration was not a plausible one. It was just way too big.
  10. cianfa72

    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...
  11. I

    I Time Dilation Near a Black Hole: Accelerating Objects Approaching the Event Horizon

    First of all, I wish everyone a Happy New Year. I am interested in your expertise on a special constellation, which I will first briefly describe. If you observe an object that is approaching the event horizon of a black hole, it is said that at some point the distant observer will have the...
  12. M

    Tangential acceleration of proton due to a changing magnetic field

    ##\displaystyle R=\frac{mv}{qB}\implies v=\frac{RqB}{m}## where ##v## is the speed of the proton ##\displaystyle\frac{dv}{dt}=\frac{Rq}{m}\frac{dB}{dt}## On substituting the values, I get ##\displaystyle\frac{dv}{dt}=9.58\times 10^4\ m/s^2## This answer, however, is incorrect. Where have I...
  13. brotherbobby

    B Kinematic equations ##\textbf{purely}## from graphs

    1. The first equation between velocity ##v## and time ##t## can be derived using the graph I have drawn for the purpose as shown on the right. Since acceleration ##a_0## is a constant, the graph of ##v-t## is a straight line. The slope of the line is ##\dfrac{v-v_0}{t} = a_0\Rightarrow \boxed{v...
  14. MatinSAR

    Pushing a block against the wall of an elevator that is accelerating

    Easier case: Elevator is at rest. We need to prevent box from free fall so friction should be bigger than "mg".(And they can be equal) When we push with force F we know that the maximum static friction is ##u_sF##. "mg" should be smaller than ##u_sF## or should be equal to it so the minimum...
  15. L

    Inner product between velocity and acceleration is zero (parametric)

    Hi, I am having problems with task b I then defined the velocity vector and the acceleration vector as follows ##dot{\textbf{r}}'(t) = \frac{1}{||\dot{\textbf{r}}(t)||} \left(\begin{array}{c} \dot{r_1}(t) \\ \dot{r_2}(t) \end{array}\right)## and ##ddot{\textbf{r}}'(t) =...
  16. E

    Pearson HW23, The Little Prince

    A. Correct answer is radius = 1770m, acceleration = 2.73*10^-3m/s. B. I don't know how to approach this problem. I don't know if I should start with forces, energy, or basic kinematics.
  17. M

    How would we define a value for acceleration if only the direction is changing?

    How would we define a value for acceleration if only the direction is changing and not the speed?
  18. J

    B Elevator Question -- What does a downward acceleration mean?

    If an elevator is moving upward, what does a downward acceleration mean? When applying the free body diagram, will the positive direction be upwards since the elevator is moving up?
  19. P

    B Clock synchronising by clock transport?

    I have a reference system A with three clocks of the same type. Two clocks are at rest in the origin of A and could be synchronized without any problems. The third clock rests at a distance in the x-direction. Is it possible to synchronize this third clock by accelerating the second clock at...
  20. Lotto

    Movement of the water level in the barrel - calculate its velocity, etc.

    Here is only my solution: ##A_1 \frac{\mathrm d h}{\mathrm d t}=-A_2\sqrt{2hg}##, so by integrating we get ##h(t)=\left(\sqrt{h_0}-\frac{A_2}{2A_1}\sqrt{2g} t\right)^2.## Setting ##h(T)=0## we get ##T=\frac{A_1}{A_2}\sqrt{\frac{2h_0}{g}}.## By doing the first time derivative of ##h## we...
  21. I

    Force meter problems...

    I don't get how is the 4th case different from the 1st case? In both cases the weights are hanging and are not accelerating, but somehow in 4th case the force meter shows 0N while in 1st shows 10N. All other meters show 10N but the last one. Now, I don't know hot to solve last one. I tried...
  22. K

    I Acceleration in Newton's second law

    Hi, I was looking over one of the sample examples in Halliday and Resnick, the one about the scale in the elevator. There is something that bugs me about it, and I'd like to know if you agree. The example has to do with finding the reading of a scale that is measuring someone's weight in a...
  23. James1019

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    TL;DR Summary: Find initial vertically upward speed of the ball Find horizontal speed of the speed Find angle How to: Find initial vertically upward speed of the ball Find horizontal speed of the speed Find anglei try to solve it but it didn't work
  24. chwala

    Show that acceleration varies as cube of the distance given

    In my approach i have distance as ##(x)## and velocity as ##(x^{'})##, then, ##(x^{'}) = kx^2## where ##k## is a constant, then acceleration is given by, ##(x^{''}) = 2k(x) (x^{'})## ##(x^{''}) = 2k(x)(kx^2) ## ##(x^{''}) = 2k^2x^3##. Correct?
  25. Astro-Eddie

    B Where does the 1/2 in 1/2 at^2 come from?

    I am currently studying Newton's laws and mechanics. I have this question: Why is distance=half a*t^2? Where did the 1/2 come from? Can someone explain this without using calculus?
  26. Strato Incendus

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  27. yashboi123

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    The correct answer is obtained by rearranging Δ x/ Δt = v. However, I assumed there would be some acceleration in the y direction so I tried to use the kinematic equations. To find the time I simply rearranged Δ x/ Δt = v, assigning v=5.2 m/s and Δ x = 650. I assumed there is no acceleration in...
  28. ejacques

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    The acceleration near the earth, due to the force of gravity is g. Now every particle when moving in a curve trajectory had a centripetal acceleration towards the center (say the sun) a=(v^2)/R. If this is true why we measure weight only with the account of g? I guess when R is big it might be...
  29. S

    Pendulum SHO but with extra downward acceleration of the pivot

    Hey guys, Can someone help me understand how to understand this problem intuitively please? How I understand is that I need to look the acceleration relative to the lift as if it were f.e. on another planet with a different acceleration. this gives me a = g - 5. But then again if I didn't look...
  30. golya

    Relating acceleration to distance and time

    I’m an absolute beginner and I need someone to show me where I’m wrong. Knowing the formula of acceleration ∆v (change in velocity) / ∆t (change in time) where ∆v = ∆x (distance) / ∆t, a common way of relating acceleration to distance is to say a (acceleration) = (distance/time)/time =...
  31. P

    Getting the truck over the crossing

    If the truck accelerates at 1.47 fps until it reaches its top speed of 8.8 fps, then it takes approximately six seconds to reach the top speed (1.47 x 6 = 8.82). In its first six seconds, the truck covers 30.87 feet (the truck reaches 8.8 after traveling 23.2 feet). To cover the remaining 57.13...
  32. P

    When is the acceleration due to gravity negative and when is it positive?

    I know to break it down into its x and y components and then use Pythagorean: Acceleration in the x direction is Fx/m ---> (7.50 x 10^6*cos55) / (4.50 x 10^5 kg) = 9.56 m/s^2 Acceleration in the y direction is: (Fy - mg)/m ---> ((7.50 x 10^6*sin55) - (4.5 x 10^5* 9.8 m/s^2)) / (4.5 x 10^5 kg)...
  33. jaketodd

    B Any limit on how fast a Maglev can go?

    When using magnetism to accelerate the Maglev, and neglecting the usual frictions, and also relativistic effects, is there any limit how fast it can accelerate to? Or is there any sort of increasing "drag" of any sort native to magnetism, which would get in the way of acceleration, as it goes...
  34. al4n

    B Need help understanding some concepts about friction

    We have 2 objects, m1 and m[SUPlB]2[/SUB] Friction is present between the two objects but not between m1 and the floor. A force is exerted on the bottom object which causes it to accelerate parallel to the floor. The thing I'm wondering for while now is, how do I prove that the acceleration of...
  35. K

    Finding acceleration of the pulley block system

    What is the initial acceleration of mass 5M .The pulleys are ideal and the string inextensible. My attempt- 2Mg-T=2Ma (for 2M) T=Ma (for M) Solving we get T=2Mg/3 T-N=5MA (for 5M) N=2MA (for 2M) Solving we get A=2g/21 but the given ans. is 2g/23
  36. F

    I 3 clocks thought experiment - Absolute vs. relative aspects?

    Here are two similar, quite simple thought experiments, followed by assumptions on final clock readings. In the end, my most important question to them. Exp1: - we have two space ships, ss1 and ss2, both have clocks on board, named cl1 and cl2 - we have a third clock, cl3, somewhere located in...
  37. H

    Calculation of Box's Acceleration on a Trailer with Friction

    Question picture: My solution: Where: S is the lineforce Ff is the force as a result of friction a is the resulting acceleration F is the acting force The answear is supposed to be a=(F-2mg(mu))/(m+M) Any idea what i could have missed? Thanks for your help on beforehand!
  38. M

    Electron in a time variable magnetic field

    TL;DR Summary: Find acceleration of electron in dB/dt >0 Hello. Here is a problem that i'm not so sure about: Inside a solenoid there is a time-dipendent magnetic field B, so we have dB/dt = b (constant). We want to know the acceleration of an electron: a) placed in the center of the solenoid...
  39. E

    I Sabine Hossenfelder says time dilation is due to acceleration

    Sabine Hossenfelder says time dilation is due to acceleration in the twin's paradox. Is this true? At 12 minutes into this video , Hossenfelder states, "This is the real time dilation. It comes from acceleration." Looking at the equations for time dilation, time dilation comes from...
  40. acertainayush

    Experimentally calculating the acceleration due to gravity

    [Mentors' note: No template because the thread was moved from the technical forums] TL;DR Summary: I need help with determining the value of 'g' using the data I have collected in the lab, using an apparatus consisting of light gates fixated on a stand, the positions of which can be varied...
  41. Ben2

    Rise of Liquid from Horizontal Acceleration

    The only way I get this is to make a the vertical acceleration at the bottom corner and g the horizontal acceleration there. This is from Halliday & Resnick's Physics. I've been unable to find anything there or in REA's Physics Problem Solver. Thanks for any hints submitted.
  42. P

    Finding the apparent acceleration due to gravity versus latitude

    I began by drawing a diagram and resolving the forces. Since the question asked for 'apparent gravity' I tried to find the normal force. I started with the equations: $$\\(\frac{GM}{R^2}-N)sin\lambda-Fsin\lambda=m\omega^2Rcos\lambda$$ $$\\(\frac{GM}{R^2}-N)sin\lambda-Fcos\lambda=0$$ Solving...
  43. orangephysik

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    Hi. I need help with part a). I calculated the wavelength of the source by using the formula f_0 = v_phasefront / λ and got λ = (343 m/s) / (520 Hz) = 0.6596 m. And then I set up an equation for the velocity of the source v(t) = a*t (with v(t = 0 )= 0 m/s) and s(t) = 1/2 * at^2 + s_0. But I...
  44. C

    Solving Distance Traveled Using Formulas vs. Graphs

    So basically I wonder why the distance traveled by a body in the 5th second gives different results when calculated by the formula for accelerating body(##d=V_0\times t + \frac{1}{2}\times at^{2}##) and when calculated using a graph(formula for the surface of the triangle). Here is the graph of...
  45. L

    Angular acceleration problem for a pulley used to raise an elevator

    I tried to multiply 1/8 g (1.22625) by the radius (1.25 m) and got 1.53 rad/s^2. This is actually the linear acceleration of the elevator. How do I get the angular acceleration of the disk? Thanks!
  46. A

    Question involving angular acceleration of a spinning wheel

    wfinal=98.0 rad/s, dt=3.00s w=(37 revs/3)=>w=(37 revs*(2*pi/1))/3=>w=77.493 a=(98-77.493)/3=>a=6.8357 My answer is exactly half of the correct answer. Where did I go wrong?
  47. A

    Rocket acceleration problem: confused about Newton's 2nd Law

    TL;DR Summary: I approach a rocket acceleration problem using two approaches: F=d(m*v)/dt and F=ma. The resulting differential equations are different. What am I doing wrong? We have a ship with a mass-reaction rocket engine floating in space. The initial mass of the ship (including fuel) is...
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