All Questions
Tagged with acceleration calculus
97
questions
1
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1
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431
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Expressing acceleration in terms of velocity and derivative of velocity with respect to position
we know that
$$a = \dfrac{dv}{dt}$$
dividing numerator and denominator by $dx$, we get $$a=v\dfrac{dv}{dx}$$ provided that $dx$ is not equal to zero or instantaneous velocity not equal to zero
when I ...
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7
votes
6
answers
2k
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Can acceleration depend linearly on velocity?
Is it possible that acceleration may vary linearly with velocity. Is it practically possible, if so is there a practical example of it?
By integration I was able to verify that for the above case to ...
- 121
1
vote
3
answers
62
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Motion in a plane situation
There is something weird I find about the following situation. Suppose a particle has the $X$-coordinate $= 2+2t+4t²$ and $Y$-coordinate $= 4t+8t²$. So it's velocity in $X$ is $2+8t$ and velocity in $...
- 45
0
votes
2
answers
74
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Confusion Unit of Acceleration
I have been reading Newtonian mechanic but I got confuse in defining the unit of acceleration that "Why is the unit of acceleration $m/s^2$"?
- 11
0
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3
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166
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Power and work contradiction
A body is starting from rest. A force is acting on it for a short period of time. In that given time, power delivered to it at any instance $t$ is given
$$P = F \cdot v_1 = ma \cdot v_1 = mv_1^2/t,$$
...
2
votes
1
answer
537
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How to determine the minimum "Arrival Distance" given a maximum velocity, acceleration and jerk along with an initial velocity and acceleration?
Problem
Given the following:
$A$ - maximum acceleration.
$J$ - constant jerk (the rate of change of acceleration).
$v$ - initial velocity.
$a$ - initial acceleration (where, in practice, $a ∈ [-A, A]$...
- 121
3
votes
4
answers
2k
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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
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0
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225
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How to determine the distance travelled before a maximum acceleration is reached given a constant jerk?
Problem
Given:
An initial velocity and acceleration of 0.
A maximum acceleration $A$
A constant jerk $J$
How might one determine the distance $D$ traversed before the maximum acceleration $A$ is ...
- 121
-1
votes
2
answers
167
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Problem in instantaneous acceleration and instantaneous velocity
Recently i came accross a problem that said
An object is dropped straight down from helicopter the object falls faster and faster but its acceleration decreases over time becoz of air resistance. the ...
- 13
2
votes
3
answers
147
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Query regarding instantaneous velocity and instantaneous acceleration
Suppose an object's velocity is $5 \ \text{m/s}$ at $t = 1$ seconds and $8 \ \text{m/sec}$ at $t = 2$ seconds then the acceleration here is $3 \ \text{m/sec$^2$}$ i.e at $t = 1$ seconds the ...
- 13
1
vote
3
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12k
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Does the SUVAT equations of motion (Kinematics) come from some differential equation?
Wikipedia says about the equations of motion that;
"If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.&...
3
votes
3
answers
357
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Calculating displacement from acceleration (intuitively) [closed]
If I say acceleration of car is constant at $4\; \rm m/s^2$.
Then isn’t it that it covers $4\; \rm m$ in $1\; \rm s$ with velocity $4\; \rm m/s$.
Then in $2\; \rm s$, the velocity is $8\; \rm m/s$. ...
- 725
0
votes
3
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417
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What is correct definition of tangential acceleration?
Is tangential acceleration the rate of change of magnitude of velocity
OR,
Is it simply the rate of change of velocity?
I am asking this because I am sort of confused, because there is no tangential ...
0
votes
3
answers
1k
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How does gradient give $g$?
How is
$$g=-\nabla V$$
where $V$ is gravitational potential and $g$ is acceleration due to gravity.
I am new to calculus.
0
votes
1
answer
858
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Convert Acceleration-Time Graph to Velocity Time Graph [closed]
I have a set of 40 readings that make up 2 seconds of simple harmonic motion of an extension spring and I would like to use these readings to come up with a graph and if possible a function that ...
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