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,




{\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.

View More On Wikipedia.org
  1. B

    Graphing velocity, acceleration, and position

    im not sure where to start
  2. 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...
  3. 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!
  4. 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...
  5. 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...
  6. 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...
  7. 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.
  8. 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...
  9. orangephysik

    Doppler effect and acceleration of source

    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...
  10. 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...
  11. 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!
  12. 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?
  13. 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...
  14. Remle

    Acceleration & Normal Force of a Box: 4 m/s2 & 418 N

    What is the acceleration of the box? Paper says the answer is 4 m/s2. What is the Normal force acting on the box? Paper says the answer is 418 N. I know that for most cases FN=Fg=W. So, by definition the "original" Normal force is 245.25 N (am I correct?) I calculated the Fay which is...
  15. kielbasa

    I How does the mass of the wheels affect the car's acceleration?

    Hi, I found this interesting thread, https://www.physicsforums.com/threads/accelerating-a-car-including-the-moment-of-inertia-of-the-wheels.930374/ but as it has been closed to replies, I decided to ask here. The thread ended up with the equation: where τ - 200Nm engine torque provided on...
  16. A

    Friction, Mass and Acceleration: Analyzing Block Motion

    The block starts to slide if friction can no longer hold the block. F=u*n and F=(m1+m2)a so: (m1+m2)a=uN=>am1+am2=uN=>am2=(uN)/(am1) So:am2=(uN)/(am1) is the force. The answer is F=(u*m1g(m1+m2))/m2 I do not see how the acceleration terms are canceled. Is my answer equivalent to this?
  17. brotherbobby

    B In uniform acceleration, mean velocity ##\bar v = \frac{v_0+v}{2}##?

    Question : For uniformly accelerated motion ##a(t)=a_0\;\; \forall \text{times}\;t##, we can say that the average velocity for the entire motion ##\bar v = \frac{v_0+v}{2}##, where ##v(t)## is the final velocity at some time ##t## and ##v_0## is the initial velocity. How do we show that? Issue...
  18. C

    Angle of acceleration in non-uniform circular motion

    For (c), Solution is Can someone please explain how they calculated that angle? I thought they would do ##arc\tan (\frac {32}{3.35})## Many thanks!
  19. C

    Points of inflection on acceleration graph

    EDIT: For this part(b) of this problem, The solution is However, isn't there more points of inflection than just ##t = 3,5 s ##? Points of inflection is when ##x'' = a = 0## so it should be ## 3 ≤ t ≤ 5 s## I also have a question about part(d): The solution is However, could I tried...
  20. chwala

    Find the total time taken and acceleration in the given problem-Kinematics

    This is the question; I made some math error...then i just realised this is an easy problem...anyway, i know you guys may have an alternative approach to this; kindly share... For part (a) i have; ##a=\dfrac{10}{t_1}## and ##2a=\dfrac{20-10}{(t_1+t_2)-t_1}##...
  21. paulimerci

    A or B? Increase in Velocity Backwards & Acceleration Forward

    I've understood that between time t=0 to t=1 sec (moving backward), the object is moving with increasing velocity in the negative direction, slows down, and comes to rest at t = 1 sec. At t = 1 sec, the object returns to its starting position, briefly rests, and then begins to accelerate (moving...
  22. N

    Acceleration of Uranium 238 ion through a potential difference

    I don't understand why the Uranium 238 ions are accelerated I think ##\Delta V = -2000 V## to accelerate since the ion would be accelerated by more postive charges so ## V_i > V_f ##
  23. N

    What exactly is wrong here? (F=ma when Force and acceleration are zero)

    If F = 0 then a = 0. When the equation is written in the form F = m*a, it appears ok, that whatever the mass be, LHS and RHS of the equation are equal so no problem. But when the same equation is written in the form m = F/a, then m becomes undefined when F = 0 and a = 0. It occurs to me that...
  24. paulimerci

    Which statement is true? (Velocity and Acceleration of a Tennis Ball)

    I understand that when a tennis ball is in motion, the velocity vectors and acceleration vectors are pointing in the same direction. When the ball slows down, it is decelerating and comes to a stop. In the above statement, I understand that from the given angle, both vectors are pointing in the...
  25. baumbad

    Given a Constant Acceleration magnitude of g/4, Find the value of t

    I got to the quadratic equation of the motion where: 4gt^(2) - g(delta t)t - g(delta t) = 0 and tried to solve for t. In this case, we would take the positive discriminate since we are dealing with the passing of time. t = ((sqrt(17) g(delta t)) + g (delta t)) / (8g) However, this is the...
  26. S

    Does the gravitational rate of acceleration increase within a planet?

    Example: The radius of the Earth is 6371 km. It has an average density of 5.5 g/cm3. Earth's inner core has the highest density at 12.9 g/cm3 [more than double the average]. Its surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared. It may...
  27. S

    Engineering How do I know that the angular acceleration is the same for both wheels?

    how do I know that both angular accelerations are the same for both wheels here? should I apply relative motion analysis for the acceleration at A(with ##a_x,A and a_y,A##) and B(with ##a_{x,B} and a_{y,B}##) here, or is just a_A=r*alpha_C and a_B = r*alpha_D enough from which a_A=a_B and thus...
  28. N

    I How can I calculate length contraction for accelerated motion?

    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...
  29. matthewphilip

    B Very basic acceleration problem (from a video on The Physics Classroom website)

    I'm confused after 2 minutes of this video on acceleration; It starts with telling us that a car acclerates at 8m/s/s for 5 seconds. Then it gives a data chart which includes the car's position at each time interval. The data is as follows. O seconds; O metres 1 second; 4 metres 2 seconds; 16...
  30. iceninja3

    Find acceleration of Moving incline with a block on it

    My attempt: As I need to find acceleration I believe that I need to use F=ma(and thus draw a free body diagram). I drew the block's weight components(mgsinθ, mgcosθ) and concluded that the only force acting on the plane in the horizontal direction is the horizontal component of...
  31. iceninja3

    Finding acceleration from Velocity vs Position graph

    The answer is E. I was initially very confused as to why the answer was not A but realized that the graph was velocity vs position (rather than velocity vs time) which means I can't simply take the derivative of the given graph. One thing I tried was writing out the equation first(c being a...
  32. String theory guy

    Acceleration of a suitcase in an accelerating train after getting pushed

    I was doing one of MIT's 8.01.1x course and came across this question. In case 2, how would we be able to theoretically calculate the horizontal acceleration in this non-inertial frame? The course said that Newton's Law do not hold in accelerating frames. However, could we find the...
  33. Z

    Motion with Time-Dependent Angular Acceleration

    I am not understanding how to even start the question
  34. Z

    Motion with constant angular acceleration

    I am not understanding the 2nd part of the question where it is asked about how many revolutions will the blade make when it reaches full speed. Please help
  35. N

    Weird Thing About Coriolis Acceleration and Coriolis Force?

  36. H

    Finding linear acceleration of a spool and cable

    My angular acceleration is wrong but all I had done was torque which was 110 NM / I = 930 kg-m^2 and calculated 0.118 rad/s^2. But because this is wrong I am stuck and I have no idea how to find angular velocity to plug into the equation to find linear acceleration.
  37. PhysicsRock

    Leaking cart being accelerated

    My approach is to use the definition of the Force with ##\displaystyle F = \frac{dp}{dt} = \dot{m} v + m \dot{v}##. Since ##m(t)## decreases linearly, I should be able to set ##m(t) = M - \Phi t##, thus ##F = - \Phi v + (M - \Phi t) \dot{v}##, which gives ##\displaystyle v = -\frac{ F - (M -...
  38. redirmigician

    I About Direct Laser Acceleration

    How does this Lawson–Woodward theorem work. I read on the wiki that the particles cannot be accelerated by lasers. But I do see acceleration of electrons with free space. I wonder how this is done. https://rdcu.be/c0fRw http://dx.doi.org/10.1103/PhysRevAccelBeams.19.021303 In addition, I have...
  39. paulimerci

    Find the acceleration of the system (2 blocks sliding on a table)

    In both the cases 7 kg mass accelerates towards the right because of the 50N force. The unbalanced forces in both the cases are the force of gravity due to 5kg block and force of friction. Applying Newton's second law of motion to cases 1 and 2 yields the following results for acceleration...
  40. redirmigician

    I Acceleration in an electron field

    I read something about accelerators using nanotubes. I am a little concerned about the design mentioned in the "High Density with Perpendicular Carbon Nanotubes" part of this paper(https://doi.org/10.3390/photonics8060216). Can wakefield acceleration be done in an electron field? Or maybe I...
  41. M

    Kinematics of movement subject to a variable acceleration

    Can someone guide me how can I find time ?! I don't have any idea. This is a part of a question in Classical Dynamics.
  42. mastermechanic

    I Vertical acceleration of the water bubbles in a kettle?

    Question is simple, as we all know water boils at the bottom surface and it forms tiny bubbles. These bubbles grow up and rise in the water until they detach. What is the acceleration of these bubbles compared to gravitational acceleration? - Is it constant velocity? - Is it approximately...
  43. PhysicsRock

    Solving an Inertial Mystery: Angular Acceleration and Mud

    So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall...
  44. neilparker62

    B Fundamental Problems With Exam Question: Moving Truck & Acceleration

    Is it just me or are there some fundamental problems with this exam question ? What is driving me bananas is you have a moving truck (constant velocity). Then the truck "accelerates" but the block in the back of the truck "stays in the same place". Does this mean relative to the ground...
  45. crememars

    Acceleration required for ship to avoid crashing into another ship

    I drew a x(t) graph to try to map out what was going on. I guessed that in order to just barely avoid the crash, the velocity of Enterprise (v.e) will have to decrease to match the velocity of Klingon (v.k). So v.e final = v.k Since we're looking for the acceleration, I used this formula: vf^2...
  46. T

    Integration of acceleration in polar coordinates

    I made this exercise up to acquire more skill with polar coordinates. The idea is you're given the acceleration vector and have to find the position vector corresponding to it, working in reverse of the image. My attempts are the following, I proceed using 3 "independent" methods just as you...
  47. S

    Understanding how time derivative = acceleration

    I'm having a hard time understanding some concepts and would really appreciate some help(not super smart so I need some things basically dumbed down). In my physics lab we're going over Newton's Second Law. There's a statement in the lab papers I don't understand. It states "As you should know...
  48. P

    Acceleration of a person jumping off of a bathroom scale

    fnet=ma Fn-fg=ma 840 - (72)(-9.8) = 72a a= 840 - (-705.6) /72 a=21.19m/s^2 The correct answer is 1.9m/s^2 unsure of how to get that
  49. huc369

    B Acceleration -- How is the intermediate displacement speed derived?

    I don't know if I wrote it correctly
  50. huc369

    B Can anyone tell me some formulas for acceleration?

    我是一名高中生,对加速度的一些计算感到困惑,请与我分享一些信息 (translation by the Mentors via Google Translate): "I am a high school student and confused about some calculations of acceleration please share some information with me"