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.

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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
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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
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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
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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
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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
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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
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0answers
78 views

Angular velocity of a unit vector given spherical angles

Consider the unit vector of $$ \check{n} = \begin{bmatrix} \sin \phi \sin\gamma \\ \cos \phi\\ \sin \phi \cos\gamma \end{bmatrix} \, . \tag{1} $$ ...
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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=...
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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
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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 ...
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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 ...
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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
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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
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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 ...
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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 ...
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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.
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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
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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 ...
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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
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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
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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 = \...
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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 ...
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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. $...
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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, ...
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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 ...
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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 ...
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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 ...
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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
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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
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\left<0,v\right>$. ...
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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 ...
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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
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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
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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 ...
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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
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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 $0.215$ ...
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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
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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 ...
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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}...
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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 ...
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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 ...
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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
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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
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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
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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 ...
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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 ...