# Questions tagged [kinematics]

The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.

456 questions
Filter by
Sorted by
Tagged with
84k views

### Why does kinetic energy increase quadratically, not linearly, with speed?

As Wikipedia says: [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$. Why does this not increase linearly with speed? Why does it take so ...
• 3,207
84k views

### Recommendations for good Newtonian mechanics and kinematics books

What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.?
22k views

### Why are objects at rest in motion through spacetime at the speed of light? [closed]

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ...
• 4,607
217k views

### How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
• 633
2k views

### Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
• 331
132k views

### How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
• 1,517
15k views

### Understanding terms Twist and Wrench

In kinematics, physics and especially robotics, we often encounter the terms Twist and Wrench. Twist is (LinearVelocity, AngularVelocity) and Wrench is (Force, Torque). The reason I'm confused is I ...
• 505
4k views

### Why does the amount of energy transferred depend on distance rather than time? [duplicate]

The change in energy of an object can be determined by the work equation, where work is the change in energy: $$W = F \cdot d$$ I conceptualize the transfer of energy as simply a series of small "...
3k views

### Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light?

I have found these two formulas: $v = at + v_0$ $x = \frac{1}{2}at^2 + v_0t + x_0$ a is the acceleration v is the velocity x is the position t is the time $v_0$ is the initial velocity $x_0$ is the ...
• 1,613
4k views

### Elastic collision between two circles [duplicate]

I am trying to calculate the final velocities of two equal mass 2-dimensional circles after an elastic collision. I have tried to figure it out using formulas I know from high school physics, but ...
27k views

### Speed of a fly inside a car [duplicate]

A couple of weeks ago I was travelling in a car (120 km/h approximately) and I saw a fly flying in front of me (inside the car, near my nose, windows closed). I wonder how was that possible. Does it ...
• 225
3k views

### Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?

Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity ...
• 165
59k views

### How can an object's instantaneous speed be zero and it's instantaneous acceleration be nonzero?

I'm studying for my upcoming physics course and ran across this concept - I'd love an explanation.
• 203
6k views

### Integrating radial free fall in Newtonian gravity [duplicate]

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
• 93
834 views

### Why is the kinetic energy for non-relativistic velocities not described by $KE=mc^2$?

Today, I learned that the kinetic energy of an object can be described by $$KE=\gamma mc^2=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}mc^2.$$ I have been taught in school that the kinetic energy of an object ...
• 3,778
4k views

### What is the position as a function of time for a mass falling down a cycloid curve?

In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems. If we consider $x$ the horizontal axis and $y$ the vertical ...
• 183
43k views

### How to prove that a motion is Simple Harmonic Motion (SHM)?

I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you ...
• 151
152k views

### Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?

I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ...
• 422
2k views

### Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
• 141
3k views

### Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
• 3,097
2k views

### Are velocity and acceleration smooth quantities?

My thinking: acceleration corresponds to a force which is instantaneous, so the acceleration of a rigid body can be rather spiky (non-smooth) velocity (angular velocity) describes the ratio of ...
• 123
13k views

### Is it possible to have a rate of change of acceleration?

I know this may seem a weird question, but it always bothers me. My physics book (Resnick,Halliday,Walker), and also various sites never say anything beyond acceleration. But when a moving body is ...
23k views

### How can kinetic energy be proportional to the square of velocity, when velocity is relative?

Let's start with kinetic energy (from los Wikipedias) The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a ...
• 411
2k views

### Physics of simple collisions

I'm building a physics simulator for a graphics course, and so far I have it implementing gravitational and Coulomb forces. I want to add collisions next, but I'm not exactly sure how to go about ...
• 151
190k views

### What is the difference between "kinematics" and "dynamics"?

I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics". I first encountered this in Jackson's E&M book, where, in ...
• 9,551
7k views

### How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
• 661
3k views

### Physical intuition for higher order derivatives

Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
• 202
1k views

### How do I adjust the kinematic equations to avoid reaching speeds faster than light?

I like some 'science' in my 'science fiction', so I started crunching out the kinematic equations for some of the scenarios my characters are getting involved in, and ran smack dab into an issue. (...
• 133
2k views

### Tangential acceleration in circular motion?

A lot of my problems have objects moving in circular paths with tangential and normal components of acceleration. If the tangential component is non-zero though, the speed is changing so the radius ...
• 2,009
71k views

### Difference between momentum and kinetic energy

From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
• 1,181
17k views

### Why do rain drops fall with a constant velocity?

While reading my physics book. I came across a line that says that: Rain drop falls with a constant velocity because the weight(which is the force of gravity acting on body) of the drop is balanced ...
4k views

### Should you run when under rain?

When it's raining, would you get less wet if you run or more wet? I think you will get less wet, because rain is coming down in a constant volume and if you run you will have a shorter amount of time ...
• 327
10k views

### Why does a balloon spiral in the air instead of moving in a straight line?

When an air-filled balloon is released without its opening tied up, it moves in a circular path rather than a straight line. Why is that?
1k views

### The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available

If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
• 365
5k views

### The usage of chain rule in physics

I often see in physics that, we say that we can multiply infinitesimals to use chain rule. For example, $$\frac{dv}{dt} = \frac{dv}{dx} \cdot v(t)$$ But, what bothers me about this is that it raises ...
117k views

### Why does a ball bounce lower?

If a ball hits the floor after an acceleration then why does it bounces lower? I mean the Energy is passed to the floor then why does the floor give back less Energy?
• 989
10k views

### Can an object *immediately* start moving at a high velocity?

What I mean is, suppose a ball is fired from a cannon. Suppose the ball is moving at 100 m/s in the first second. Would the ball have started from 1m/s to 2m/s and gradually arrived at 100m/s? And is ...
38k views

### Why does work equal force times distance? [duplicate]

My book says: Energy is the capacity to do work and work is the product of net force and the 1-dimensional distance it made a body travel while constantly affecting it. This seems quite ...
• 503
3k views

### How does anything move? [duplicate]

So in order for two things $A$ and $B$ to move apart, for example, relative to each other, $B$ can be set into motion away from $A$. This means that we have to increase $B$'s velocity and therefore ...
11k views

### What is displacement? Position relative to a reference point or change of position

What is the "official" or most useful definition of displacement in the context of kinematics? There are two common ones: Displacement is the length and direction of a line from a fixed reference ...
• 133
8k views

### Is there a scalar acceleration?

The magnitude of Velocity is simply Speed. On the other hand, the magnitude of Displacement seems to be a simpler idea than Distance. And the magnitude of Acceleration is not the change of Speed over ...
3k views

### Why is speed defined like it is?

I have a rather basic, maybe even dumb, question. I was wondering why speed is defined as it is: $s = d/t$ Of course, what the equation means is not too difficult to understand. However, there are ...
• 954
10k views

### Uniform Circular Motion

Why does the object not go inward, into the circle if the acceleration is inward? I think its because the velocity to outward? So they sort of cancel each other out? But if the speed is kept constant ...
• 495
1 vote
520 views

### Is the derivative of the magnitude of a position vector the speed? Is the integral of the speed the magnitude of a position vector?

I'm reading a book titled "Introduction to Mechanics" by Kleppner, and I came across an example: A bead moves along the spoke of a wheel at constant speed $u$ meters per second. The wheel ...
• 113
358 views

### Momentum diagram for two colliding Particles

I'm trying to learn how to draw a momentum diagram but I didn't find any specific method to do so. I following the The Geometry of space-time by Tevian Dray. What I know is that The geometry of 2-...
• 11.9k
12k views

### Why does a perpendicular force not change speed?

I have been taught that a perpendicular force acting on an object will only change the direction of its velocity, not its magnitude. The explanation that was provided to me is that because there no ...
9k views

### Static Friction - Only thing that can accelerate a train?

I'm a computer programmer that never studied physics in school and now it's coming back to bite me a bit in some of the stuff I'm being asked to program. I'm trying to self study some physics and I'...
• 223
26k views

### Why is average velocity the midpoint of initial and final velocity under constant acceleration?

Since average velocity is defined as$^1$ $$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$ where $\vec{\mathbf x}$ denotes position, why is this quantity equal to \...
• 103