Questions tagged [kinematics]
For questions on the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.
-1
votes
0answers
33 views
Distance traveled from velocity as function of position
I was given this equation:
$$v(s)=7,5*\sqrt{1-0.03*s}$$
How do I find the distance traveled after 3/4 of an hour, assuming that velocity is in km/h and s in km.
I've tried:
$$v=\frac{ds}{dt}$$
$$...
0
votes
3answers
46 views
Find projectile speed given maximum height and range.
I want to simulate a catapult throwing a rock in my computer game, but by design, I want all my units to shoot from a certain height, reach a maximum height and also hit a target that can be meters or ...
1
vote
1answer
33 views
Basic algebra for semi-elastic collision
Consider two point masses involved in a semi-elastic impact:
Suppose the two point masses are moving parallel to each other with the velocities $v_1\neq v_2$ (and no external forces/accelerations). ...
0
votes
1answer
16 views
Finding initial (vertical) velocity from a vector - projectile motion
Only a starting point $(p)$ and initial velocity $(v)$ is given in a form of cartesian points $(p.x, p.y)$ and $(v.x, v.y)$. I want to find the equation of the parabola going though them so then I can ...
1
vote
1answer
46 views
Help showing Frenet-Serret Formulas with respect to $t$
The Frenet-Serret Formulas involve a unit tangent vector,
$$\hat T = \frac{\vec r’(t)}{||\vec r’(t)||}$$
and a unit normal vector (differentiating with respect to $t$)
$$\hat N = \frac{\vec T’(t)}{||\...
1
vote
1answer
29 views
3 particles A,B and C are situated at the vertices..
I had this question
"3 particles A,B and C are situated at the vertices of an equilateral triangle ABC of side d at t=0. Each particle moves with a constant speed v. A always has its velocity along ...
1
vote
0answers
78 views
Angular velocity of a unit vector given spherical angles
Consider the unit vector of
$$
\check{n} = \begin{bmatrix} \sin \phi \sin\gamma \\ \cos \phi\\ \sin \phi \cos\gamma \end{bmatrix} \, . \tag{1}
$$
...
1
vote
1answer
26 views
Kinematics and the parametrization of a curve
An object moves along a path given by the equation
$$ y(x)=2x^{2}-3x-11$$
with a constant speed of 5m/s. Find the velocity at x=2.
My approach:
We know that the speed of the object is given by
$$ 25=...
1
vote
2answers
55 views
Calculating Launch Angle Given Distance with Added Height (which itself depends on launch angle)
In my physics class we have learned to calculate a desired launch angle to allow a projectile to hit a target given the target’s distance away and the initial velocity.
Now in this case the initial ...
0
votes
1answer
29 views
Particle traveling on a helix
In this problem, we consider a particle moving on a helix:
a) Suppose the position vector of a particle as a function of time $t$ is given by $r(t) = ( \cos t, \sin t, 3t )$. Find the speed of the ...
1
vote
1answer
44 views
How to go about solving a basic mechanics problem?
The bus leaves the bus stop with an acceleration of 1.5 m.s^-2 which is mantained until it reaches the speed of 12 m.s^-1. At the same instant a girl who is 5 m away from the bus stop starts to run ...
0
votes
0answers
34 views
Find joints positions in 3D robotic manipulator?
I have been trying to solve this 3D mechanics problem, but can't seem to be able to figure out what the best way to do it is.
I have this $3D$ robot manipulator with $3$ rotary joints $(B, C, D)$. I ...
0
votes
2answers
52 views
A city bus travels the distance between two stops
A city bus travels the distance between two stops, moving on schedule, with an average speed of 30 km/h. One day he got into a jam, so the average speed, with which it travelled, was 5 km/h less than ...
0
votes
1answer
41 views
Jerk-controlled minimal time second-order velocity smoothing problem.
Kinematic profile:
$T1$ - increasing acceleration time (max jerk)
$T2$ - constant acceleration time (zero jerk)
$T3$ - decreasing acceleration time (-max jerk)
Jerk, acceleration, velocity
The ...
1
vote
1answer
20 views
Finding a future co-linear midpoint of two moving objects
I have three objects in a 2d space: S, E1, and E2.
E1 and E2 are at some location ((E1x, E1y) & (E2x, E2y)) and moving at constant velocities VE1 and VE2. They will be set initially and not ...
1
vote
2answers
17 views
Relationship between angle of banked road and normal force and its component
Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
1
vote
1answer
27 views
Kinematics of a disc
So the kinematics of the contact point of a disc rolling without slip in a Cartesian plane if fairly straightforward. The velocity for the contact point is just
v = ω r ev
where r is the wheel radius ...
0
votes
1answer
20 views
Solving simultaneous equations for motion
Textbook asked student to solve the following simultaneous equations where x is distance in cm and t is time in minutes:
x = 2t
x = -4t -20
I multiplied equation 1 by the 't' coefficient of ...
1
vote
1answer
50 views
Maximizing a pool's length
A math project I am doing asks the following:
Blammo is to be fired at ground level with a muzzle velocity of $35$ m/s over a flaming wall that is $15$ m high and a ground level shark pool. The pool ...
0
votes
1answer
37 views
Physics with Kinematics and Projectile motion
A $0.1$ kg nut is thrown by a squirrel off of the top of a $10$ m tall tree. It is thrown with an initial upward velocity of $4$ m/s and an initial horizontal velocity of $3$ m/s.
a) How long till ...
0
votes
1answer
27 views
Special curves in geometry and kinematics
Let us consider a particle $\vec{w} = (w_1,w_2,w_3)$ in three dimensional space, whose trajectory is parametrized by the spherical coordinate system $(\rho,\theta,\varphi)$:
\begin{equation*}
w_1 = \...
0
votes
1answer
67 views
Projectile Motion with Wind Effect
My first question is about the former question Projectile Motion with Air Resistance and Wind 1, could you suggest a book or article and an example given about wind effect.
My second question is ...
1
vote
0answers
22 views
The distance it will take a car to reach a certain speed, constant acceleration
In 10 seconds car can accelerate to 100km/h. Let's say acceleration is constant, calculate the distance it will take the car to reach 90 km/h after leaving a built-up area where it was moving 60km/h. $...
0
votes
1answer
54 views
Relating Turning Angle To Arc
I am trying to determine how to relate the turning angle of a vehicle to an arc. For the purposes of this vehicle, I am not taking into account Ackerman Steering, so for the intent of this question, ...
1
vote
2answers
89 views
Connected rates of change kite problem
A boy is flying a kite. The boy is running into the wind at a steady speed of 3 m s−1, with the kite flying directly downwind of the boy. At one instant, the length of the string between the child and ...
0
votes
0answers
25 views
I've been having trouble finding the angle in order to maximize horizontal distance when you have a change in vertical position of $-1\mathrm{m}$. [duplicate]
Here's the problem: Ms. Soloveichik throws a ball with an initial velocity of $v_i$ at a height of exactly $1$ meter above where the ball will land. At what angle relative to the horizontal should ...
1
vote
0answers
29 views
One question: I guess it's to do with suvat equations:Kinematics [closed]
A car moves along a straight horizontal road from a point A to a point B, where AB = 885 m. The car accelerates from rest at A to a speed of 15 m s −1 at a constant rate a m s−2. The time for which ...
1
vote
1answer
21 views
Surjectivity of momentum mapping
I have to show that the following mapping of momenta is surjective. The mapping $\{p_i^{\mu},p_j^{\mu},p_k^{\mu}\}\rightarrow\{\tilde{p}_{ij}^{\mu},\tilde{p}_k^{\mu}\}$ is given by
$$
\tilde{p}_k^{\...
2
votes
1answer
179 views
velocity and acceleration in a parabola
A particle moves with constant speed along a parabola of equation $y^{2}=2px$ with $p=constant$. I want to find its velocity and acceleration vector.
Since the velocity magnitude is constant I know ...
0
votes
1answer
72 views
How to graph the motion of a projectile?
Suppose I have a projectile, fired at angle $\theta$, with velocity $v_0$, assuming it's only acted upon by gravity. How can I find an equation to enable me to plot the motion (vertical height against ...
1
vote
1answer
40 views
Swimming to a Boat [closed]
A boat is travelling on a bearing of $α=60^\circ$
at a constant speed $u=3.0$ $m/s$.
A man is swimming at a constant speed $v$
in order to reach the boat from a point a distance $l=100\ m$
due east ...
1
vote
1answer
33 views
Find acceleration of a particle when given a velocity function in terms of displacement.
Particle B moves such that its velocity $v\>ms^{-1}$ is related to its
displacement $s\>$m, by the equation $v(s)=arcsin(\sqrt{s})$. Find
the acceleration of particle B when $s=0.1 $m.
My ...
1
vote
1answer
42 views
kinematics .. how to solve this question. shouldn't acceleration be 0 when velocity is 0?
a particle moves in a straight line so that , t s after passing through a fixed pointO , its velocity, v m/s, is given by v=2t-11-(6/(t+1)). find the acceleration of the particle when it is at ...
0
votes
1answer
60 views
Showing that $x(t)=at^2$, $y(t)=vt-at^2$ parameterizes a parabola
Solving a physics problem I obtained following motion equations
$$ x(t) = at^2 $$
$$ y(t) = vt - a t^2 $$
And I want to determine what type of curve is it on the interval of $\left<0,v\right>$. ...
1
vote
0answers
28 views
Theoretical mechanics - Inverse Kinematicss
On theoretical mechanics essay at the university, I have stumbled in the issue below:
Given $\textbf{u}^T \textbf{D}(\mathbf{\theta}, \alpha)\textbf{v}(\textbf{d}) = \textbf{m}(\textbf{d})$, find out ...
0
votes
1answer
84 views
What is the initial acceleration of three particle at the vertex of an equilateral triangle moving towards its neighbor?
I came across this question which, asks,
3 particles, at the corner of an equilateral triangle of side s, start moving with constant speed v, such that each always heads directly towards its ...
5
votes
2answers
76 views
a cyclist travels 30 km in one hour [duplicate]
a cyclist travels 30 km in one hour
1) Demonstrate that there is an interval of 10 minutes such that the cyclist has traveled 5 Km
2) Is there always a time interval of 40 minutes during which he ...
0
votes
1answer
24 views
Physics force system find acceleration
Given this setup, how far does the book slide? This is a fairly basic kinematics problem once you have acceleration, which you can get with application of Newton's 1st and 2nd laws. Which is what I ...
-3
votes
3answers
452 views
How can i solve for time in fourth kinematic formula? [closed]
The fourth kinematic formula says that;
$\Delta x = vt + \frac{1}{2}at^2$
Where:
$\Delta x =$ Displacement
$v = $ Initial velocity
$t =$ Time
$a =$ Acceleration (Note that acceleration needs to ...
2
votes
2answers
126 views
How can I find the magnitude of the acceleration in this $2$-D motion kinematic equation?
Can someone help me plug in the correct variables for this $2$-D motion problem?
So the problem is: A puck moves $2.35 \frac{m}{s}$ in a $-22.0^\circ$ direction. A hockey stick pushes it for $0.215$ ...
1
vote
2answers
95 views
Get acceleration from distance and speed [closed]
I want to know how fast an object with the speed s1 (2.77m/s) would have to deccelarate to reach a speed s2 (0m/s) within a certain distance d (2.35m). With a formula for that I could go on to ...
0
votes
1answer
32 views
Calculate distance travelled with non-constant speed after time t
Let's Imagine such a situation.
A man is walking for the first hour with a speed of $4km/h$.
The next hour he is jogging, with the speed of $9km/h$
Finally, after two hours, he starts to run, with the ...
0
votes
2answers
52 views
Fastest possible time for Rectilinear Commuter Train
Say one has a train on a track between two stations with four constraints:
$a_a$ = Acceleration of the Train.
$a_b$ = Braking/Deceleration of the Train.
D = Distance between the two stations.
$v_{max}...
1
vote
0answers
46 views
Eulerian and Lagrangian descriptions of velocity
I feel as if I understand the conceptual difference between Lagrangian and Eulerian descriptions. But I can't seem to follow the math. I have one example that I would greatly appreciate an explanation ...
1
vote
2answers
268 views
solution to the differential equation $ma=mg-kv^2$ (free fall)
The differential equation $ma=mg-kv^2$ is to describe the motion of a particle that is falling from a tall building, and the air resistance is proportional to the square of the velocity of the ...
1
vote
2answers
152 views
Four cars A,B,C,D are moving at constant speeds on the same road
I need help solving the following problem:
Four cars A,B,C,D are moving at constant speeds on the same road (not necessarily in the same direction). Car A passed car B at 8 a.m. and car C at 9 a.m. ...
0
votes
1answer
64 views
vector acceleration question
The question goes: A rifle is fired with angle of elevation $36^{\circ}$. What is the muzzle speed if the maximum height of the bullet is 1600ft?
I ignored the x-component and cared only y-component....
0
votes
1answer
46 views
Angular velocity of Earth from the perspective of coordinate system fixed to surface
I'm working my way through "Vector Analysis and Cartesian Tensors by Bourne & Kendall, and I got stuck on problem 3.29.
Wouldn't an anguar velocity of an object from the point of view of a point ...
0
votes
1answer
85 views
Time to travel a given distance, given two separate, but constant acceleration and deceleration rates and a max velocity.
Problem
I need to calculate the minimum time, t, it takes to travel a given distance, x.
Constraints and Known Variables
Distance x is broken up into two distinct, known segments:
xv = vacuum ...
1
vote
1answer
87 views
Given $\frac{dx}{dt} = f(x)$, find $x(t)$
I have a phase plot of velocity vs position in 1D. I don't, however, have an equation for it--as this one can change for different applications. I want to find the corresponding function x(t).
For my ...
