All Questions
35 questions
-1
votes
3
answers
99
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Explaining the equations of motion in kinematics [closed]
Hi I Have these equations and I don't know and understand what each of them means.
Can someone help me?
$$\tag 1 v=v_0+at$$
$$\tag 2 x=v_0t+\frac{at^{2}}{2}$$
$$\tag 3 v^{2}=v_0^{2}+2ax$$
What does ...
- 7
14
votes
4
answers
2k
views
Why doesn't constant acceleration give me total displacement?
I started learning 1D kinematics and learnt definitions of constant velocity and constant acceleration. I thought that if a particle is changing its velocity uniformly then it has constant ...
- 177
0
votes
4
answers
213
views
Why acceleration is not always parallel to velocity but velocity is always parallel to displacement? [closed]
Velocity is derivative of displacement :
$$\vec v=\frac{\mathrm {d\vec r}}{\mathrm dt}$$
And acceleration is derivative of velocity.
$$\vec a=\frac{\mathrm {d\vec v}}{\mathrm dt}$$
Given that their ...
- 325
-1
votes
1
answer
66
views
Interpretation of velocity-velocity and acceleration-acceleration curves
I am parametrizing equations of motion in the form:
$$x(t) = x_0+v_{0,x}t\\y(t) = y_0+v_{0,y}t+\frac{1}{2}at^2$$
The parametrized equation with respect to time:
$$y(x) = y_0+v_{0,y}\cdot \frac{x - x_0}...
- 145
1
vote
1
answer
66
views
How can i find the angle? [closed]
Here we have a question of a 2 dimensional movement. I know that it is needed to get its second derivatives for acceleration but then what should I do?
- 13
3
votes
2
answers
160
views
Acceleration in terms of displacement
I am having problems understanding the derivation of acceleration in terms of displacement. The first step is fine:
$$a(x) = \frac{\mathrm dv(x)}{\mathrm dt}
= \frac{\mathrm dv(x)}{\mathrm dx} \frac{\...
- 131
1
vote
1
answer
143
views
How to know which solution is physical?
When solving the expression for displacement of an accelerating object and solving for the time variable:
$$v_it+\frac{1}{2}at^2=d$$
$$v_it+\frac{1}{2}at^2-d=0$$
$$t=\frac{-v_i\pm \sqrt{v^2_i+2ad}}{a}$...
user324326
0
votes
3
answers
67
views
Different equation is given for "position"
$$s=ut+\frac{1}{2}at^2$$
Assuming, $u=0$
$$s=\frac{1}{2}at^2$$
$$a=\frac{2s}{t^2}$$
So I got a function for acceleration.
$$v=u+at$$
$$v=\frac{2s}{t} \tag{1}$$
In reality I know that $s=vt$ when ...
- 91
0
votes
1
answer
363
views
Paradox in the Kinematic SUVAT Equations of Motion
The 5 equations of motion have been chosen such that from the 5 variables of motion: $s$, $u$, $v$, $a$ and $t$; each equation, exclusively omits one of these. This allows us to only ever require the ...
- 129
1
vote
2
answers
1k
views
Why is position proportional to time squared?
Now I know some of the obvious answers to this, such as if you integrate the acceleration twice, you’ll get time squared, but what I’m really looking for is more of an intuitive answer.
One of the ...
- 11
0
votes
2
answers
891
views
How can I calculate acceleration from displacement and time?
How can I calculate acceleration from displacement and time, assuming a velocity at rest? Is there any formula to do so?
- 103
3
votes
3
answers
3k
views
How do acceleration, velocity, and displacement affect/relate to eachother?
I have been wondering this since learning about position, velocity, and acceleration vs time graphs but can't put numbers/equations to it.
I know that acceleration acts to change velocity, shown by ...
- 169
0
votes
1
answer
40
views
Can accelaration of a falling mass be positive when upwards direction is positive? What am I missing?
As shown in the figure:
(+) direction is upwards
displacement is y
time=t
Let's say that $ y=30-5t^{2} $ , thus the second derivative will give acceleration as -10 which is (-) as expected.
Now let'...
3
votes
4
answers
3k
views
If displacement is 0, does that mean initial velocity equals final velocity?
For instance, one of the kinematic equations is :
$$v_f^2 = v_i^2 + 2ad$$
where $v_f$ is final velocity, $v_i$ is initial velocity, $a$ is acceleration, and $d$ is displacement.
Say for instance a guy ...
- 33
0
votes
2
answers
234
views
How to find velocity and acceleration at a point given acceleration in terms of position [closed]
A particle moves along a horizontal straight line with an acceleration $𝑎=6 𝑠^{1/3} m/s^{2}$. When $t = 2 s$, its displacement $S = 27 m$ and its velocity $v = 27 m/s$. Calculate the velocity and ...
- 242
0
votes
2
answers
85
views
Kinematic displacement: why not represent higher order rates of change?
I understand that the equation for kinematic displacement is:
$x = v_{0x}t+\frac{1}{2}a_xt^2$
Perhaps my understanding is naive, but it seems like this leaves out higher order rates of change. Why ...
- 111
0
votes
1
answer
2k
views
What does the area under an acceleration-displacement curve represent?
Considering the equation where,
$$
\frac {1}{2} \left (v^2_f - v^2_i \right) = \int_0^s ads\,
$$
What does the left-hand side of the equation actually represent? Is there an intuitive explanation ...
- 5
1
vote
3
answers
2k
views
How do I calculate final velocity from acceleration, displacement and inital velocity?
How do I calculate the final velocity ($v_f$) given a known constant acceleration ($a$), a known inital and final position ($x_i$ and $x_f$), and a known inital velocity ($v_i$), where $v_i$ can be ...
- 21
1
vote
2
answers
429
views
How can I understand if an object stay (zero velocity) or moving with constant velocity (zero acceleration)
I thought a scenario like; lets say I am looking an object and there is nothing except this object. Is there a way to understand that if this object is stay on its position or if object moving with a ...
- 181
0
votes
6
answers
4k
views
What does a negative acceleration mean? Is the object slowing down, changing direction, or both?
I am confused about such things as negative velocity, acceleration, and displacement and what the negative indicates.
- 29
0
votes
1
answer
92
views
In the equation for acceleration (with known $v$, $u$ and $s$) why velocity is squared and displacement is multiplied by 2? [closed]
In the following equation $$a = \frac{v^2 − u^2 } {2s} ,$$ where $v$ is the final velocity, $u$ is the initial velocity, and $s$ is displacement. Why is velocity squared and displacement multiplied by ...
- 1
0
votes
2
answers
734
views
Confusion on Horizontal & Vertical Components of a Parabolic Motion
This was a question I found about projectile motion, the question was what's the bike's speed when it took off.
Using $S=ut + 0.5at^2$, the time taken to reach the ground is $0.505 s$, they used ...
- 1
0
votes
0
answers
95
views
Acceleration as the second derivative of displacement function
Let $x$ be displacement as a function of time $t$ and some other physical quantity $k$ such that
$ x = f(t,k) $
Now,
1) Will the acceleration $a$ be $\frac{\partial^2 x}{\partial t^2}$ or $\frac{d^...
- 23
4
votes
3
answers
513
views
Does Euler number $e$ have a role in kinematics?
Euler number $e$ is often explained with the example of compound continuous interest.
I was wondering if it could also be illustrated with an example about the displacement of a body (although not an ...
- 527
0
votes
3
answers
819
views
Calculating acceleration from displacement measurements
I have a table of measurements s(t):
t[s], s[m]
0, 0
12.48, 26.4
18.06, 52.8
22.32, 79.2
I have calculated all values for $a$ using
$$ a=\frac{2s}{t^2} $$
and simply sticking the values into the ...
- 393
0
votes
2
answers
1k
views
Condition of acceleration when using $x=vt$
So my teacher told me that since $v = \delta x/ \delta t$, $\delta x = v • \delta t$ (naturally), and that is equal to the "area under the velocity-time graph", or displacement. This all makes sense ...
- 157
0
votes
2
answers
104
views
Extraneous Negative and positive velocities
Consider the following question:
A rock falls from a 500m high cliff and is accelerated downwards at $10~ \text{ms}^{-2}$. What is the velocity at which it hits the ground if we ignore air ...
-3
votes
2
answers
60
views
If x is the position, how and why is one sure that a is displacement and b is acceleration in the given equation? x=a+bt²
I don't understand why a and b have to be displacement and acceleration respectively. Is that because of kinematics fist equation v-u+at?
-1
votes
1
answer
1k
views
Finding kinematic equation with time-varying acceleration
I would like to obtain a relation between initial velocity and distance covered till velocity is zero, with time varying acceleration. For a constant acceleration we can solve:
\begin{align*}
\int_{0}^...
- 99
1
vote
1
answer
138
views
Acceleration to Displacement
I'm doing an experimental program.
I've a smartphone fixed on the car dashboard with a support, during the travel i read from an application some value from inertial sensor,
Precisely I read,
...
- 11
-1
votes
1
answer
140
views
Displacement on a turn with constant speed with a pitfall
A car is driving North-West on a highway. It has a
speed of $20 $ m/s with the cruise control on.
Ten seconds later, the car is heading North-East (still going $20 $ m/s).
Determine the ...
- 113
0
votes
2
answers
276
views
Calculating mobile displacement based on acceleration
I have written a mobile app that measures x y z accelerations. I am trying to convert the acceleration results into displacement but dont think a simple $d=\frac 1 2 {a {t^2}}$ will do the job. We ...
- 109
1
vote
1
answer
4k
views
How to use accelaration data of moving object to calculate distance?
I read couple of similar question on this forum and few blogs on web, though I am still confused,I am determined to calculate object displacement using accelerometer data.
So, I tried using www....
- 131
0
votes
2
answers
6k
views
A problem says : a car starts from rest and undergoes a constant acceleration. It travels 5 m in the....? [closed]
A problem says :
A car starts from rest and undergoes a constant acceleration. It travels 5 m in the t interval 0 s to 1 s, find the displacement of the car during the time interval from 1 s to 2 ...
- 131
2
votes
2
answers
15k
views
Calculate displacement in position from knowing constant acceleration
I have recently started studying physics at school, and my teacher went over the following equation without explaining about it too much:
$$s=\upsilon_{0}t+\frac{1}{2}a t^2
$$
I have wondered, why ...
- 137