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.
I'm trying to calculate the theoretical minimum thickness of an "ideal foam" for a given jerk and acceleration limit.
Say we have a ball in free fall from 1.83 meter, reaching 6 m/s. It then reaches an "ideal foam" for decelerating it. I'm trying to understand the connection between the...
Here's what I've tried. First of all, I assume that q is positive. For particle A, then, I can write $$q E -k {\left( x _{A }-x _{B }\right) }=m \ddot{x }_{A }, $$ where ##x _{A } ## and ##x _{B } ## are the coordinates of the particles relative to their equilibrium positions from the point of...
A clock is set up to continuously broadcast its indicated time via radio waves to non accelerating observers in different inertial frames of reference.
The clock is accelerated and its tick rate is observed to decrease by all observers relative to the tick rates of their local clocks. Its...
If 2 synchronised clocks at the same location in space (away from any gravitational field) are equally accelerated away from each other and then equally accelerated back together to the original location will they then indicate the same time?
I don't seem to understand the difference of accelerations when a cord is wrapped around cylinders and spheres. What I was taught is that if the cord is wrapped around a cylinder/sphere, the acceleration of the cord and whatever it is connected to will be twice the acceleration of the cylinder...
I don't really get why applying different forces to objects of different masses would result in different accelerations. I read my textbook, and I understand the formula F(net) = m*a, and I think the reason may be because mass is inversely proportional to acceleration ? But this doesn't really...
Above is a graph of the distance vs. time for car moving along a road. According the graph, at which of the following times would the automobile have been accelerating positively?
OK, so I was able to get that at t=5 and t=29, it's accelerating positively (I graphed the velocity vs time graph...
okay I annotated the diagram given and the grey thing where they take y axis up as positive is what I understand to be, right?
But in the answers, they start off by going V = u - gt. They've taken acceleration due to gravity as a negative value. Why? I thought the skateboarder was falling...
I'm struggling to get to the correct answer, which I posted down bellow.
The pulleys are ideal, so I figured that m₁ and m₂ will both move upwards (towards the ceiling?) with the acceleration a, while m₃ will move downwards with the acceleration -a.
Let T be the tension in the string which...
According to the problem statement: $$a = \frac{dv}{dt} = const \implies dt = \frac{dv}{a} \implies \int_{0}^{T} \,dt = \frac{1}{a} \int_{0}^{v_f} \,dv \implies T = \frac{v_f}{a}$$ Now, the distance covered is given by, $$L = \int_{0}^{T} v \,dt \implies L = \frac{1}{a} \int_{0}^{v_f} v \,dv...
Initially I thought a good strategy for solving the problem would be to find the torque on the pulley to get alpha (angular acceleration) and then use alpha to find the tangential acceleration of the pulley which is equal to the block's acceleration. I'm not sure if this is correct.
Let ##...
Hi,
starting from a recent thread in this section, I decided to start a new thread about the following:
Take a generic irrotational/zero vorticity timelike congruence. Do the 4-velocity and the direction of proper acceleration (i.e. the vector in that direction at each point with norm 1)...
Imagine making a hole in the ground, about a mile deep, with a large and square diameter. In the middle of the hole, there is a hollow and narrow tube with all air sucked out. Next to one of the walls, so close that it's touching, there is another hollow tube without air inside. Two identical...
I conceptually know how to solve this problem, what I struggle with is the direction of the acceleration.
For example to solve the first question I need to find the horizontal displacement when the ball hits the ground.
Therefore ##l_0= x(t_1)= x_0 + v_0 t_1##, where ##t_1## is the moment the...
I need to determine:
1) The initial acceleration of the disk
2) the speed of the disk when the spring reaches minimum displacement
For point one I think I should use the free body diagram and then ##\Sigma F = ma##, I'm taking as positive the right and the upward directions and the counter...
I need to determine:
1) The accelerations of both the slab and the block, the moment right after the spring was released.
=> I can consider Fspring as a constant force. Both bodies can be considered as points of mass.
I'm taking as positive the left direction. I've analyzed both objects using...
In my working i have;
For a)
##\tan 55^{\circ} = \dfrac{450}{R}##
##R = \dfrac{450}{\tan 55^{\circ} }= 315 N##
part b) no problem here ...horizontal to left.
c) This is where my real doubt is,
i have using sine rule;
##\dfrac{9.8}{sin 55^{\circ} }= \dfrac{a}{sin 35^{\circ}}##
##a =...
Here is my question
Imagine if you had an object, this object is then accelerated. The process of acceleration bends space-time. For a black hole to form there must be extreme curvature of spacetime. Therefore, accelerating an object at such a high rate could create a black hole.
I am not...
When there is an explosion, matter flies off in every direction. At first it is static, and then it accelerates, and keeps accelerating, until friction slows it down to a stop. In a vacuum would this matter continue to accelerate indefinitely? And could this be the cause of the continued...
When you shake back and forth AC gaussmeter ,he significantly increase reading(magnetic field), because device is moved in Earth static magnetic field.
Does his acceleration or velocity cause increase in reading and why he even increase reading if magnetic field from Earth is static and...
My guess was simply that as acceleration changes from the north to east direction, the total magnitude change of v is ##v \sqrt 2##.
Acceleration is ##\mu g##, so time would be ##\frac {v \sqrt 2} {\mu g}##. This agrees with the textbook solution.
What I do not understand is the trajectory...
I understand based on the equation F = ma that if there is no acceleration, the forces on the object all balance out to 0 in all directions.
What I don't get is for example, slowly lowering a heavy stone slab at a constant velocity v, and raising it way above my head as high as I can at a...
This is the problem set. I am stuck from this point... If anyone could give me a hand I would really appreciate it. I know this is probably really simple, but I don't know any of this and have been trying my best with youtube, and other peoples posts.
PS this is for high school
If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed.
What is going on here?
My initial approach to this question was breaking the components of acceleration in the x and y axes and applying the three equations of motion to find the final velocity as well as the final position. As we were expected to find the net final velocity of the particle, I found the resultant of...
Doesn't friction always oppose the motion?
From the clockwise rotation here, shouldn't the cylinder be moving to the right? so why are the acceleration and friction in the same direction to the right, and in the same direction as the motion?
(attached image for reference)
i solved it like this...
s = ut + 1/2 at^2
t= 1.08 (from part a)
u= 65 sin4.30
a= 9.81? or -9.81
the answer said -9.81
why? wouldn't acceleration change from -9.81 to +9.81 because it moves up then down???
its soo confusing...
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...
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...
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}=...
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.
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.
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...
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...
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...
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...
##\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...
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...
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...
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) =...
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.
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?
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...
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...