# What is Constant acceleration: Definition and 340 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. ### In a constant acceleration motion, Is it possible to have constant speed?

I think it's not possible. In 3D for constant acceleration we have : ##\vec v = \vec v_0 + \vec a t## It's a line in 3 dimension so velocity's magnitude(speed) is changing with time. I appreciate any better idea.
2. ### I Find the constant acceleration of an object that slows down to a standstill

Hi all, Let V be an initial velocity, D any distance, and T a time duration. which algorithm allows to obtain a constant acceleration A that make the object to brake from V to a zero speed over D during T? Thanks
3. ### 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...
4. ### Relative motion with constant acceleration

I think the question is wrong. My answer : But it should be wrong because : I think the question is wrong … But I'm not sure …
5. ### Reasoning/evaluation: Free fall motion with constant acceleration

My guess is that I could compare it to the time interval of the free fall motion(stage2). Would that be enough to let it make ‘sense’? As we know that stage 1 has an acceleration of 16m/s^2 and free fall one of 9.81m/s^2. Then.. is it sufficient to reason that the time needed to complete stage...
6. ### A particle motion problem in the x-y plane with constant acceleration

I have attempted but I don’t get anywhere.
7. ### B No way to catch up with galaxies currently receding at >c?

Consider a far-away galaxy that is considered to be currently receding from Earth at 2x the speed of light. (With this 2x c recession velocity, we are speaking of the Vnow, the imputed relative velocity of the galaxy compared to Earth now, not the velocity of the galaxy relative to Earth at the...
8. ### Constant acceleration in a rocket

I thought I'd start by writing the problem in a tensor formalism. I have identified with ##S## the Earth and ##S'## the rocket. Since the acceleration provided is in the rocket's frame of reference, I can write the following four-vector. $$a'^\mu=(0, a, 0, 0)$$ Since we are interested in the...
9. ### Average speed with constant acceleration over a period of time

Say that we have an instance where something falls down from a certain height with constant acceleration g. We know that the average speed with regards to the time period is less than (u+v)/2 since we spend less time at the higher speeds. How do we actually calculate the average speed over a...
10. ### I Solve Constant Acceleration Problem in Special Relativity

Basically I just want to work out a constant acceleration problem in relativity, of the same kind of introductory physics. Vo= 0.9999c Vf = 0 D= 50 Au Accel, Earth frame? Accel, Ship frame? Time of transit, Earth frame? Time of transit, ship frame? Motion is 1-D. All origins line up at the...
11. ### Mechanics problem — Car moving with constant acceleration

I tried this but I don't know if it makes sense: Average velocity from A to B = 22/2 = 11m/s Average velocity from B to C = 104/4 = 26m/s (26-11)/6 = 3.75m/s
12. ### Constant Acceleration -- Equation for Vavge

Initially we are given the statement Vav = (x-x0)/t, so far so good. But, we encounter the following paragraph... "We can also get a second expression for Vav that is valid only when the acceleration is constant, so that the v-t graph is a straight line (as in Fig 2-14 - [I've omitted the graph...
13. ### 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...
14. ### Feeling Forces (like feeling gravity while in free-fall)

a = (change in magnitude of velocity) + (change in direction of velocity) → Can you feel when you change direction? Even if force and acceleration are constant? ↑ ↓ ↑ ↓ ↑ ↓ o
15. ### MHB How Does Constant Acceleration Affect Car Speed Over Time?

2.3.16 A car is traveling at $45 \, km/h$ at time $t=0$ It accelerates at a constant rate of $10 \, km/h\, s$ (a) How fast is the care going at $t=1\, s$? $$v_t=v_0+at=45+10(1)=55\,\dfrac{km}{h}$$ at $t=2\,s$ $$v_t=v_0+at=45+10(2)=45+20=60\,\dfrac{km}{h}$$ (b) What is its speed at a...
16. ### Calculating the Displacement (Having Constant Acceleration)

I'm just having trouble understanding 1) how to plug in the formulas correctly and 2) the correct manner of attacking this. I feel like I'm missing something basic/simple. Any help is greatly appreciated! So far I've got: D = (0) + .5(2.2m/s^2 x 2.4s)^2 Enrique
17. ### Quadratic equation help (Time when one vehicle passes another)

Sample Problem 2.04 Drag race of car and motorcycle I was following all the way up to using the quadratic equation for this problem...(please see img for a more detailed attempt at a solution.) So I may have simplified incorrectly here: but I came up with 2.8t^2-(58.8)t+408.1=0 but when...
18. ### Performance data of a car owned by a student....

Hi. My question is for now why the equation of x as a function of time for phase of motion ab is ##x=50t-375##? Shouldn't that be ##x=375+50t##?
19. ### A glider of length 12.4 cm moves on an air track

Homework Statement Serway Physics - P2.40 A glider of length 12.4 cm moves on an air track with constant acceleration (Fig P2.39). A time interval of 0.628 s elapses between the moment when its front end passes a fixed point A along the track and the moment when its back end passes this pont...
20. ### 1D Angular Motion with different velocity stages

Homework Statement I am solving a kinematic problem, where I have a link that is attached to a rotational joint. I need to find the position of the joint for t=0..8, and I need to do it for every 0.01s. The problem comes from the fact that I have three stages for the velocity, during t = 0..0.1...
21. ### Objects approaching one another with uniform acceleration

Homework Statement persons 1 & 2 are initially at rest (vi=0m/s) 48m (d) apart. they then run towards each other at constant accelerations person 1 acceleration = 0.50m/s2 person 2 acceleration = 0.30m/s2 how long until they reach each other/collide (t)? at the instant they collide, how far...
22. ### Electron in constant acceleration

If I throw the electron from electron gun with some acceleration .Will it maintain it's constant acceleration? If yes then it radiates photons from where will the electron gets energy to constantly radiate photon? If not then why?
23. ### Circular Constant Acceleration Formula

A constant tangential force of magnitude 12N is applied to the rim of a stationary, uniform circular flywheel of mass 100kg and radius 0.5m. Find the speed at which the flywheel is rotating after it has completed 25 revolutions? I know that this can be done using work-energy. But since a...
24. ### Energy to achieve constant acceleration - F=ma and 1/2mv^2

I was in a discussion regarding the time it took to get to the speed of light with a constant acceleration of 1g, and the time was something close to a year. (ignoring all the other major factors ). Just from a Newtonian perspective, if you have a 100kg rocket putting out 900N of thrust, you...
25. ### In how many seconds will the n-th wagon pass next to me?

Homework Statement Train starts to travel in a straight line at increasing speeds. The first wagon passes next to me in 4 seconds. In how many seconds will the n-th wagon pass next to me? Homework Equations s= vo.t + 1/2at^2 v= vo + at The Attempt at a Solution First of all we didn't learn...
26. ### Need help with this question regarding kinematics.

Homework Statement a) A ball is thrown in the -y direction off of a cliff with a velocity of 7m/s. If the ball takes 1.45s to reach the ground, how high off of the ground is the cliff? (Answer: -20m) Homework Equations Vf=Vi+a(t) Displacement=Vi(t)+1/2a(t)^2 Vf^2=Vi^2+2a(Displacement)...
27. ### B Help with constant acceleration under special relativity

Hi, I am trying to wrap my brain around special relativity equations but I'm struggling with the math. I am a computer programmer comfortable with the algebra and but never studied calculus or physics. Say I am already traveling at velocity "v" where "v" is approaching the speed of light. I...
28. ### I Relativistic formula for motion with constant acceleration

Suppose a comet F ,at 1 AU distance, is traveling toward a massive body (a neutron star or other) with v= .99 c, suppose also that a = 3 km/s^2 and (to simplify calcs) that it is uniform from there to the star. It will hit the star after ca. 1000 seconds and its speed should equal C: 297*10^9...
29. ### Riding a bicycle around a tree w/ constant acceleration

Homework Statement African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a tree this size. If, starting from rest, you travel a distance of 162 m around the tree with a constant angular acceleration of 5.00 × 10–2 rad/s2, what will your final angular...
30. ### Special relativity - constant acceleration

Homework Statement A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...
31. ### Finding constant acceleration without time

Homework Statement [/B] An X-ray tube gives electrons constant acceleration over a distance of 14 cm . If their final speed is 1.0×107 m/s , what are the electrons' acceleration? Express your answer to two significant figures and include the appropriate units. Homework Equations My prof. has...
32. ### MHB How Does Constant Acceleration Affect Antelope Speed Over 70 Meters?

An antelope moving with constant acceleration covers the distance between two points $\textbf{70.0m}$ apart in $\textbf{7.00s}$ Its speed as it passes the second point is $\textbf{15.00 m/s}$. What is its speed at the first point? The answer to this is 5 m/s ok this should be real simple but...
33. L

### Constant acceleration except time?

Homework Statement Homework Equations d = vit + 1/2at^2 The Attempt at a Solution Hey, so what i did was different from the answer key above. Instead of (4/5)^2 i did 1/ (4/5^2) so i got 25/16 as the answer. I'm not sure why tb/ta = 4/5 since 4/5 the time is referring to runner b's time...
34. ### Constant acceleration and radius of curvature

Homework Statement Homework Equations The Attempt at a Solution The normal acceleration of the particle at any instant is given by an = v2/r . v is the speed at any time and r is the radius of curvature . Minimum radius will occur when ratio v2/an is minimum . I think this will occur when...
35. A

### Positive or negative final velocity? Constant acceleration

Homework Statement A car is moving with a constant velocity of 18 m/s for 5 seconds, if in the next 5 seconds it travels a distance of 40 m, what is its final velocity? Homework Equations Δx= vit+ 1/2 at^2 vf= vi+at vf^2 = vi^2 + 2a (Δx) The Attempt at a Solution So I tried doing it different...
36. ### How Long Does It Take a Car to Overtake a Truck?

Homework Statement A car, length 2.4m, traveling at 26m/s wants to pass a large truck, length 12m, also traveling at 26m/s. If the car can accelerate at 4.4m/s2, how much time will it take the car to pass the truck (note the back of the car has to be in front of the truck)? How far will the car...
37. S

### Constant acceleration changes direction twice

Hello, I just did a practice physics problem that asked if an object with constant acceleration can change direction twice. The answer was no. What if you had an object attached to a string spinning at constant velocity. Is the tangential acceleration constant?
38. J

### Constant velocity, constant acceleration?

Homework Statement Hi, I have a quick question about an experiment I am doing. I did an experiment where I rolled a ball over a flat surface and dropped a ball from a height, and I was asked if the ball rolling over the flat surface (1-d) motion is subject to constant velocity? I was also...
39. G

### A hot air balloon rises at a constant acceleration

Homework Statement A hot air balloon is released from the ground & rises up with a constant acceleration of 4 m/s^2. When it is 16 meters above a sandbag is dropped. What is the time taken for the sandbag to hit the ground? Homework Equations v^2=u^2+2as v=u+atThe Attempt at a Solution...
40. M

### Whether constant acceleration and zero acceleration are the same

In the equation v=u+at, u=5 m/sec and a=0, then v=5 m/sec. That means the body is moving with a constant velocity of 5 m/sec. In a velocity-time graph, the equation produces a straight horizontal line. Some texts say the body is moving with zero acceleration and others say it is moving with...
41. A

### Why Earth has constant acceleration?

according to f=GMm/r^2 if force changes based on a distance between 2 objects, so during free fall object is constantly changing its distance, so does that mean the Earth is exerting a non-constant force on that object? if that was right, why's that object accelerate at a constant rate of...
42. ### Frictionless ring sliding on circle in constant acceleration

Homework Statement A box is sliding with constant acceleration a to the right. Inside the box there is a quarter of a circle upon which a frictionless ring can slide. Find the angle theta in terms of the other given variables. Picture in solution Homework Equations F=ma, etc. basic stuff...
43. ### What constant acceleration do you need to catch up?

Homework Statement Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m/s. If you start 0.91 m behind the cockroach with an initial speed of 0.82 m/s toward it, what...
44. ### Constant acceleration of baseball problem

Homework Statement "The fastest measured pitched baseball left the pitcher's hand at the speed of 45 m/s. If the pitcher was in contact with the ball over a distance of 1.50m and produced constant acceleration, (a) what acceleration did he give the ball, and (b) how much time did it take him to...
45. ### Constant Acceleration: find time

Homework Statement A man was driving a car at 78 km/h, he saw a deer at the distance of 101m, how much time is needed so that the car slows down after it drove 99m and stops. Homework Equations Δx = 1/2 (vi + vf) * t The Attempt at a Solution I'm thinking about finding the Δx
46. ### Why do both Block A and B have a zero acceleration in this scenario?

1. Homework Statement 3 blocks A,B and C are attached between them by massless and frictionless strings , that passes through frictionless , massless pullies , the blocks A and B have the same weight 25 N and the same coefficient of kinetic friction 0.35 , the bloc C goes down with a constant...
47. ### Shouldb constant acceleration when simulating magnus effect?

I am coding a game in which I desire a projectile to undergo realistic curving when rotating while moving through the air. Let's consider the instance of a projectile that is initially moving forward while spinning clockwise along an axis placed vertically in it is center of mass. The object...
48. ### Applying Newton's Laws, motion with constant acceleration

Homework Statement Homework Equations F=m*a ΣF=0 The Attempt at a Solution Firstly, I tried to work on the normal force of bowling ball. But I can't get the answer. I don't get the idea that bowling ball could be kept at constant height, I didn't really understand the question guess. Can...
49. ### A falling stone takes 0.28 s to travel past a window 2.2 m...

Homework Statement A falling stone takes 0.28 s to travel past a window 2.2 m tall. From what height above the top of the window did the stone fall? So from this problem I think I have these variables: vo = ? (or 0 because falling usually indicates 0 for an initial velocity?) yo = 0 y = 2.2m...
50. ### Simple constant acceleration/equation of motion question

Homework Statement A 747 Jumbo Jet must reach a speed of 290km/h by the end of the runway to lift off. The 15L-33R runway at Toronto International Airport is 2,770 meters long. The main Toronto Island Airport runway 08-26 is 1216 meters long. Assuming the jet has a constant acceleration, for...