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.

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60
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16answers
14k 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 $mv^2/2$. Why does this not increase linearly with speed? Why does it take so much ...
36
votes
5answers
13k views

How effective is speeding?

At a simple level, speeding in a car attempts to minimize the time required to travel a distance by utilizing the basic relationship: $$d=st$$ So for a given distance, time should be inversely ...
28
votes
11answers
34k 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 ...
16
votes
6answers
15k 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, ...
15
votes
5answers
350 views

Does the mass point move?

There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., ...
14
votes
1answer
286 views

Modelling the movement and jumps of a chalk while drawing a dashed line on a blackboard

You probably know that if you try to draw a line using a piece of chalk on a blackboard , under some conditions (for example, $\alpha<\frac{\pi}{2}$ in the picture below) you will have a dashed ...
13
votes
7answers
3k 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 ...
10
votes
1answer
553 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 $d=\frac{1}{2}at^2$?
9
votes
5answers
323 views

What is the best path for a given initial and final state?

I am trying to calculate an efficient acceleration curve given starting and final positions and velocities. I'm assuming no friction, and that the acceleration can be applied in any direction at any ...
8
votes
4answers
19k views

What is the relationship between kinetic energy and momentum?

I can't seem to figure out the relationship between $E_k$ and $p$ or $F$. I understand that the units are pretty different. But for example: A bullet with a mass of 10.0g is moving at the speed of ...
8
votes
2answers
795 views

Non-Constant Acceleration due to Gravity

Recently, I had the first physics lab for my university physics course. This lab was fairly simple, as we were merely using a computer and a distance sensor to graph the position, velocity, and ...
8
votes
2answers
411 views

Is acceleration an average?

Background I'm new to physics and math. I stopped studying both of them in high-school, and I wish I hadn't. I'm pursuing study in both topics for personal interest. Today, I'm learning about ...
8
votes
4answers
723 views

Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...
8
votes
3answers
731 views

Number of planks required to stop the bullet [closed]

A bullet looses (1/n)th of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be? Logically, to me the answer seems to be infinity, as always a ...
8
votes
2answers
265 views

What is the physical meaning of $|f''(\xi )|\leq\frac{4(f(b)-f(a))}{(b-a)^{2}}$ where $f(t)$ is position as a function of time?

Here is the full problem: I was able to prove the given expression; but the interpretation part is giving me a bit of trouble. Here is my interpretation: The average acceleration in $(a,b)$, is ...
8
votes
3answers
3k views

Can superconducting magnets fly (or repel the earth's core)?

If a superconducting magnet and appropriate power supply had just enough $I\cdot s$ (current $\cdot$ length) so that when it was perpendicular to the earth's magnetic field, the force of the ...
7
votes
6answers
83k views

How to calculate average speed [closed]

I recently encountered a puzzle where a person drove 120 miles at 40mph, then drove back the same 120 miles at 60mph. The average of the speeds is (40mph+60mph)/2 = 50mph, so the total trip time ...
7
votes
1answer
481 views

I reached a result concerning displacement with quantized time intervals. Am I on to something?

A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to ...
7
votes
5answers
798 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 ...
7
votes
5answers
12k 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 ...
7
votes
3answers
743 views

Intuitive meaning of factor 2 in formula of vertical throw max height $h=v^2/2g$

This is a question about a simple thing. The simplified expression for maximum height in vertical throw is $h=\frac{v^2}{2g}$ , could anyone explain intuitively (analogies are welcome) why there is a ...
7
votes
5answers
5k views

Why does work equal force times distance?

My 'government-issued' book literally 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 ...
7
votes
2answers
2k views

Galilean invariance of the Schrodinger equation

I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and here: ...
7
votes
4answers
662 views

Integrating radial free fall in Newtonian gravity

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 ...
7
votes
2answers
131 views

Why does a small object stay in one place after being shot from a big gun?

This video shows what I mean. Basically they shoot a bullet from a huge gun at an iPhone. What I don't get is why does the phone move only so little after being shot? As far as I can tell it isn't ...
7
votes
2answers
1k 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 ...
7
votes
1answer
350 views

what is the kinematics of a particle with complex mass?

particles with real-mass have time-like kinematics ($ds^2 > 0$). particles with zero-mass have light-like kinematics ($ds^2 = 0$). particles with imaginary-mass have space-like kinematics ($ds^2 < ...
7
votes
4answers
578 views

What's my weight when jumping on a bicycle from a higher to a lower ground?

Before I start defining the situation and asking a question, I'd like to make a few things clear: this is not a homework, merely a matter of personal interest and enthusiasm I am neither a ...
7
votes
2answers
1k views

Should acceleration be included in state vector of a Kalman filter?

I'm developing (actually adopting existing solution) a Kalman filter to model motion of a vehicle (UAV or automobile). The state vector will include position, velocity, and, possibly, acceleration. ...
7
votes
2answers
218 views

Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
6
votes
5answers
2k views

Can an object reverse its direction of acceleration even though it continues to move in the same direction?

Can anyone please explain me on this matter along with day to day examples?
6
votes
4answers
1k 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?
6
votes
6answers
776 views

If an object moved 5 meters in a second, how can its velocity be 10 m/s?

I am reading the tutorial on physics classroom.com, and am at Meaning of Slope for a v-t graph. It gives data for an object experiencing an acceleration: This is the corresponding chart for the ...
6
votes
1answer
78 views

What is “kinematic inversion” (from geophysics) in mathematical terms?

I am a mathematician working on a seismic imaging problem, and am currently (attempting to) read some geophysics papers (this one (Ruiz, Madariaga 2011) and this one (Di Carli, Francois-Holden, ...
6
votes
1answer
205 views

Is it possible to determine particles' velocities from their crossings on a ring?

2 particles are constrained to move in a ring. Both particles begin moving at $t=0$ from $p=0$, each particle moving in the opposite direction of the other. It is known that they are moving at ...
5
votes
16answers
13k 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.?
5
votes
5answers
6k views

Why there is a 1/2 in kinetic energy formula? [duplicate]

Possible Duplicate: Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$? Hèllo, I have a question about kinetic energy formula. As you know, in kinetic energy formula, we have: ...
5
votes
3answers
1k views

Why isn't average speed equal to displacement over time?

I'm in an introductory Physics course and I need help! During a one-hour trip, a small boat travels 80.0km north and then travels 60.0km east. What is the boat's average speed during the one-hour ...
5
votes
7answers
807 views

In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter?

Assume a point-mass $m$ is travelling in a straight line, and a force $F$ will act on $m$ (in the same direction as $m$'s velocity) over a constant distance $d$; why doesn't $m$'s velocity matter to ...
5
votes
4answers
981 views

How to brake 'beautifully'?

Sometimes when I'm driving my car, I play a "game" against myself in which I try to minimize the deceleration felt by passengers (including myself) while still braking in a reasonable short space. I ...
5
votes
4answers
349 views

How to tell if the collision is elastic or inelastic?

I'm a programmer and a game developer, not a mathematician or a physicist. So please go easy on the math :) I know two things: How to find the new velocities of two objects after an elastic ...
5
votes
2answers
432 views

Zeno’s Paradox of the Arrow

Premises And the Conclusion of the Paradox: (1) When the arrow is in a place just its own size, it’s at rest. (2) At every moment of its flight, the arrow is in a place just its own size. (3) ...
5
votes
2answers
9k 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 ...
5
votes
1answer
214 views

Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?

A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long. ...
5
votes
2answers
133 views

View from a helicopter rotor: why is the horizon distorted?

This video ("rotor panorama") was captured by a camera attached to the rotor head of a radio-controlled helicopter, with the frame rate set to the rotor's frequency. During a long segment of the ...
5
votes
2answers
1k views

Rigid body dynamics joints

I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
4
votes
2answers
1k views

Help me get out of a speeding ticket

I was driving uphill from a complete stop for a distance of .4 miles estimated to take 1 minute in a navigation app. I was pulled over right after cresting the hill. The cop had me on radar going ...
4
votes
3answers
701 views

Ball thrown from a moving train

This is not a question about throwing a ball vertically in a moving train. I am asking what would happen if I throw a ball in a horizontally in a moving train. Assume I am facing an exit door of a ...
4
votes
2answers
3k 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.
4
votes
2answers
118 views

The velocity of a cloud?

I noticed an unusually fast moving cloud this morning. My questions: What is the average velocity of a cloud on Earth? What is the greatest ever recorded cloud velocity? What factors affect the ...