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.
1. For the car to apply brakes, we have ##v^2=2ar⇒a=\frac{v^2}{2r}=μg\;\;[ma=μmg]⇒v=\sqrt{2μgr} ##
2. For the car to go in a circle ##\frac{mv^2}{r}=μmg\Rightarrow v=\sqrt{\mu gr}##.
We find from above that the maximum velocity ##v## possible to avoid a collision is ##\sqrt{2}## times as much...
I tried this problem 3 times. I only have two attempts left.
First time: Centripetal acceleration: 7560 m/s^2
Centripetal Force: 4.7 Newtons
Second time: Centripetal acceleration: 25.032
Centripetal Force: 4.7
Third Time:
Centripetal...
I calculated the average velocity in a previous problem and got 1.146788991m/s over a time of 8.72s. I know I can’t use a_ave=(Vf-Vi)/(Tf-Ti) because I don’t know the final velocity and have no way to find it. Do I multiply average velocity by time?
Summary: Non - ideal pulley question, should be easy but has got me good
Hey guys, looking for some help on this pulley question. It involves torque, and works with Newton's 2nd law in conjunction with a non-ideal pulley.
Text of question:
" When the motor in the figure below lowers the m =...
I'm struggling in the details of this exercise. Let ##S'## be the reference frame where the acceleration of the spaceship is constant, in which case we have ##u'(t')= a' t'## (since we assume no acceleration at the beginning). The rest frame of the rocket ##S## is connected to ##S'## via a...
This question showed up on my grade 12 physics test.
The problem I have with this question is that I did not know the direction that the system would accelerate in, so I just solved as though the mass on the inclined plane would accelerate the system. I expected that if it would accelerate the...
I have some difficulties trying to understand non-inertial frames.
I have problems to notice the acceleration in these cases, from an inertial reference frame and from non inertial refrence frame.
Consider the first case, if I'm on the wedge, I see that the block doesn't move so there's no...
I am trying to solve accelerations of a cart on these different slopes. I don't understand how it is possible without knowing the coefficient of friction, but my teacher says it is (very cryptically I might add). Can anyone help me understand this? Thanks.
I considered the downwards direction and left direction as negative. For ##m_1##, Newton's equations are:
##x) Fr + W_x - T=0##
##y) N - W_y =0##
For ##m_2##:
##y) T - W =0##
Then, if I replace the data, I get ##T=22.2 N## and then ##m_2=2.2 kg##.
With that, for the second question ##m_2=4.4...
What should I do? Because I have two possibilities. I have ##0=5+at## so ##-5/t =a##. But then I can also say that the acceleration is a negative because it is stopping, so I can write it like ##0=5-kt## and then ##5/t =k##
Homework Statement: A student is swinging a ball on a string overhead in a horizontal plane. The string initially has length 𝑙0 and the ball is moving with an initial speed 𝑣0 . The student decides to see how fast they
can spin the ball, so they begin moving it faster and faster with a constant...
Let m be a point test mass. Initially m has velocity Vy in the poisitive y-direction, and zero velocity in the x-direction. At time zero, m is accelerated in the positive x-direction. In the limit as the time goes to infinity, the velecity in the positive x-direction goes to the speed of...
Hello,
Newton's second law, when the mass is constant, tells us that the acceleration ##a=\frac {F}{m}## which produces a simple ODE.
The acceleration is a function that can be constant ##a= constant##, time-dependent ##a(t)##, velocity-dependent ##a(v)##, position dependent ##a(x)##, etc...
This is a homework question from my friend, I found the time but a tough differential equation occurred when I was trying to find accelaration, is there a simple solution for this?
Well, ##r(t)## in ##A## is just a vector ##(0;y)## because is tangent to the trajectory. Then, from the perspective of ##B## the particle moves in an uniform circular motion. Is this right?
The velocity from ##B## must be ##\omega##, right?
And what about acceleration?
I have a series of pulleys where the belt is running around them in a way to describe a sine curve. The pulleys are stationary and the belt is running from left to right. For every particle of the belt I can use standard formula to calculate their normal acceleration, when in contact with the...
Please could I ask for help with the following question:
Part (a) is no problem. Acceleration is the gradient of the graph in regions OA and AB which gives 3 and 0.5
Part (b), I believe, requires me to calculate the greatest and least value of the gradient of the curve in region BC
Part...
Well, what I've done so far is calculating the magnitude of velocity and acceleration replacing ##t=2## in ##\theta (t)## and ##r(t)## so I could get the expressions for ##\dot r##, ##\dot \theta##, ##\ddot r## and ##\ddot \theta##. But that's not my problem... my problem is related to the...
The question comes from a thought experiment of a rocket approaching the Earth accelerating at a constant rate of 1g from say from a hypothetical "earth like planet" near by. . we would be standing on the floor of the upright rocket as it lifts off, if we are standing on a scale, our...
From what I understand,
##a_{r} = v_{tan}^2 /r##
##a_{r} = (r\omega)^2 /r##
##a_{r} = r\omega^2##
##\omega^2 = \frac{a_{r}}{r}##
##\omega^2 = \frac{2+2t}{0.12}##
##\omega = \sqrt{\frac{2+2t}{0.12}}##
##s =\int_{0}^{2} \sqrt{\frac{2+2t}{0.12}}##
After integrating, I still can't seem to get the...
Choice D is obviously wrong therefore leaving us with choices A, B, and C. Can someone explain the relationship of the three variables stated above (mass, volume, and acceleration due to gravity)? Thank you.
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...
In a circular orbit, the 4-velocity is given by (I have already normalized it)
$$
u^{\mu} = \left(1-\frac{3M}{r}\right)^{-\frac{1}{2}} (1,0,0,\Omega)
$$Now, taking the covariant derivative, the only non vanishing term will be
$$
a^{1} = \Gamma^{1}_{00}u^{0}u^{0} + \Gamma^{1}_{33}u^{3}u^{3}
$$...
eb2
A car, start from rest, accelerates in straight line at a constant rate of $2.0 m/s^2$
How far will the car travel in 10 seconds
use
$d=vt+\dfrac{1}{2}at^2\quad v=0\quad a=2\,m/s^2\quad t=10$
then
$$d=(0)(10\, s)...
So there is a textbook physics question in which it asks us to calculate the acceleration of pulley B(which is massless). This exact question was posted and asked previously in this thread. However, it didn't discuss my doubt. To be exact, the question I have troubles with is (b)...
Hi all,
I found this problem in a new textbook I'm working through.
And my energy conservation equation was ## mg\frac {h}{2} = \frac {1}{2} I ω^2 + mg \frac {h}{2}*sin(55) ##
My solution was wrong and after checking why I found that they used cos(35) as the angle. The rest was the same.
I'm a...
I believe I know that when an object, in terms of linear motion, accelerates, it is being resisted by inertia, thus creating so called fictitious forces. Now, that said, how does angular acceleration affect spinning objects like say, a gymnast, when they spin around the axis of rotation? Do they...
The equations i got are attached below. Is it right? If yes what should we do after this. I tried solving the equations, but i did not arrive at the solution.
How can I calculate the ACCELERATION of a stationary steel ball after being hit by a moving steel ball.
I know how to get the final velocity but how long does it take to accelerate to that velocity from zero?
Does it depend on the elasticity of the materials?
I guess we need to know long did...
[Moderator's note: Spun off from previous thread due to topic change.]
Can you show me a situation where Newton says things accelerate and Einstein says they don't? Being in free fall doesn't mean things don't accelerate. I drop a ball towards the Earth and it not only accelerates but it has a...
2.3.17 At $t=5\, s$ an object is traveling at $5 \, m/s$.
At $t=8\, s$ its velocity is $-1\, m/s$
(a) Find the average acceleration for this interval.
$$a_{av}=\frac{v_2-v_1}{t_2-t_1}=\frac{\Delta v}{\Delta t}$$
So
$$a_{av}=\frac{-1-5}{8-5}=\frac{-6}{3}=-2 \, m/s$$
book answer $-2\...
2.62 An object's velocity is measured to be
$v(t)=\alpha-\beta t^2$ where $\alpha=4.00\, m/s$ and $\beta=2.00 \, m/s^3$
At $t=0$ the object is an $x=0$.
(a) Calculate the objects position and acceleration as functions of time
(b) What is the object's maximum positive displacement from the...
Both point A and B are moving in parallel in same direction, therefore rod is not rotating at this instance and angular acceleration is 0. Question states angular velocity is equal to zero.
Plugging into Angular Acceleration"AB" = r*sqr(angular velocity"AB") = 0.26m* sqr(0) = 0
[Moderator's...
I have asked this question on Stack Exchange: SE question.
I often encountered this sticker on most motorbikes (especially matic ones) [credit: cintamobil.com]:
There, when the tire pressure was measured from cold condition, the tire pressure are same regardless of loadout (29 psi and 33 psi...
"It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding"
-So F = -kd = -k(2.1) - d is 2.1 because it is the compression length
Now, since we know the d, divide it by 50, 2.1/50 = 0.042m
Basically, the spring unwinds 0.042 m 50 times for a total...
Problem Statement: A 2.0 kg cart and an 8 kg cart are connected by a relaxed, horizontal spring of spring constant 300 N/m. You pull the 8 kg cart with some constant horizontal force. The separation between the carts increases for a short time interval, then remains constant as you continue to...
I need some clarification on how the Higgs field work. The popular science explanation explains the effect on moving particles the way an object would be impacted by moving through a medium of maple syrup. I understand this is a very bad, inaccurate analogy. What I want to understand is does...
Let T be the tension in the string, a be the acceleration of
mass 2m, 2a be the acceleration of mass m
T = (m) (2a) ---eq(1)
The mass 3m will come down with acceleration
a’ = (a+2a)/2 = 3a/2
3mg - 2T = 3m . 3a/2
from equation 1
3mg - 2(2ma) = 3m . 3a/2
thus a = 6/17g
thus acceleration of 3m...
A particle, P, starts from rest at a point X and moves in a straight line with an acceleration expressed as a=4t. After 2 seconds, the particle reaches Y and it stops accelerating. The particle leaves Y with a velocity -3ms-1, and finally comes to rest at Z.
(i) Find the value of t when the...
A force of 100N applied to a body which has 5kg mass. Coefficient of static friction(μs) is 0.60 and Coefficient of kinetic friction(μk) is 0.55.
A) ##μ_{s} = 0.60##; ##μ_{k} = 0.55##
##F_{s}^{max} = F_{n}*μ_{s}##
##F_{s}^{max} = 49*0.60 (F_{n} = 9.8 \;m/sec^{2} *(5kg) = 49N)##
##F_{s}^{max}...
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
Problem Statement: A known mass at a know velocity collides on a spring of known stiffness. What is the equation that governs the deceleration of the mass, so that the force on the spring could be found?
Relevant Equations: 1/2 m*V^2 = 1/2*k*x^2 + 1/2*m*(Vo)^2
Kinetic energy of mass before...