Acceleration Definition and 1000 Threads

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...

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!

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...

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}##...

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...

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 ##

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

I am not understanding how to even start the question

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

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.

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 -...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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

I don't know if I wrote it correctly

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"

After 3,32 seconds, vt should have varied by 0,695*3,32. I have done a previous exercise where you only needed to calculate the radial acceleration in this scenario. There, I took the vt after the given time, squared it and then divided with the radius. I remember clearing that one, so in this...

PS: By the way today I had exams in Physics and this problem was the first one I had to solve :p (unlucky) The question was to find the maximum angle θ that the pendulum can reach if we know that the magnitude of the acceleration is the same when the mass is located in the highest and the lowest...

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 …

Princeton U. has a great intro to molec. behav. w. sound, but neither there or elsewhere have I found much on the initial acceleration phase. Is it assumed that movement over these nano-distances is already happening at c - and then there is just more of it ? How can a little stone you drop on a...

Wak a ball with a bat and the ball accelerates. Now under gravity, hold the ball out horizontally, let go and the ball accelerates ... without a wak. Given that gravity arises from curved space-time, I suggest further that the acceleration of the ball arises when sub-atomic particles (in the...

Impossible?!? By my estimation the equation that describes this motion is given by: $$Pt = \frac{1}{2}m{ \dot x}^2$$ or $$\dot{x} = \sqrt{\frac{2P}{m}} \sqrt{t}$$ but this implies: $$\ddot{x} = \sqrt{\frac{2P}{m}} \frac{1}{\sqrt{t}}$$ So, no matter how small we make the power, we appear...

I've been thinking about this for a while, and thought it would be nice if someone could guide me to an answer. In Newtonian mechanics, an inertial frame is coordinate system that's able to make measurements with respect to some imaginary axes attached to it. It's a well known fact that velocity...

I've calculated this. Is it correct? a=ω²R => ω=√(a/R) T(period)=1/ω=1 / (√(a/R)) f = 1/T = √(a/R) [ if a=10G=100 m/s² ; R=1m ] then: f = √(a/R) = √(100/1) = 10 hertz In angular velocity, can I just convert a=ω²R to ω=√(a/R) and write instead of ω=(2π)/T (in the first line)?

in special relativity we have moving reference frames resulting in a different flow of time in each reference frame. This we can explain because we use the fact that the speed of light is the same in all reference frames, leading to the Lorenz transformation giving the amunt of slowdown of time...

Hello, I noticed while trying to calculate the stardart gravity acceleration of the Earth that I never arrived at the defined value of 9.80665 m/s2 no matter that I calculate it with the equatorial radius, the polar radius, mean radius or the average of the equatorial and polar radius. With what...

Correct answer is (b) 0,620 ms2 My attempt: FBD Equation 1. ∑Fx=0=−ma−Wsin⁡(15)+f N=Wcos⁡15 f=Nμs=379,03N Equation 1. ma=f−Wsin⁡15 15a=379,03−203,1 a=2,20ms2 Equation 2. ∑MG=0=−Nx+f1,5 x=0,75m

There is no friction mentioned by the question so I assume the plane is frictionless but can the sphere roll without slipping if there is no friction? This is my attempt: Equation of translation motion of object A (assuming A moves upwards): TA - WA sin θ = mA . aCOM (A) TA = mA . aCOM (A) + WA...

First Assume the following basic circuit: I read in many textbooks that the electrons in the circuit are accelerated by the positive voltage and decelerated by the collisions, so the speed is constant. We also know that the circuit current is I = 10A so the power consumed is P = V * I = 100W...

I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an...

I need a little guidance on how they got the last step to derive acceleration, I can follow up till there. Any help would be greatly appreciated as I find it hard to move on unless I have understood.