$KE = \frac{1}{2}mv^2$ meaning the KE lost on impact would increase quadratically with speed, but f = ma would mean that force the wall applies to the car increases linearly with speed. So which really determines the damage to the car itself?
If a car hits a wall at a speed of $v$, and an identical car hits a wall at a speed of $2\,v$, with the kinetic energy equation $E_K = \frac{1}{2}mv^2$ (the speed goes from $v$ to $0$) the second car will lose 4 times the energy, and therefore cause 4 times the damage, but with the force equation $F = ma$ (the car hits the wall and decelerates), it will hit with 2 times the force, and cause 2 times the damage.  How can this be explained?
Add the ability to add "top questions" to Careers 2.0 Profile Allow me to add my own "top questions" too! I know, I know, the site should be more heavily weighted to answering, but sometimes, how and what people ask is important too! For example I recently asked  which I think is a fairly good question. Clearly I'm going to avoid questions where I've asked something very simple, but I know of a user or two who are implementing their own C standard libraries and the depth of those questions is important/ought to be on show.  Of course, the argument I can just look at their profile holds, but that awesome q/a might have been from a year or so ago in which case finding it is difficult. What is the "Event Horizon" of a black hole Do people sometimes get blocked by a webservice for things someone else has done with their dynamic IP-Address It is common practice for operators of web services (e.g. web sites) to block IP addresses when there was malicious traffic originating from that address.  It is also common practice that internet users don't have a static IP address but get one assigned by their ISP via DHCP.  Now I would expect that it sometimes happens that a specific IP address gets banned from a service and later that address gets assigned to another user, leaving the new user (temporarily) banned from the service for no apparent reason. However, I never had this problem or heard of someone having that problem.  Does this sometimes happen? If not, what prevents this from happening? I have some Java executable (jar) that is run my some shell script from a cron job once every night. That executable does not print log statements &quot;as usual&quot; just by printing them out in a sequential manner like line after line (print after print), but while it processes its data its printing a single line with status data and then &quot;overwrite&quot; or &quot;update&quot; just that single line over and over again, until its done with this part of processing. Examples: A common program would output something line this: Program XYZ started..&lt;cr+lf&gt; processing 1&lt;cr+lf&gt; processing 2&lt;cr+lf&gt; processing 3&lt;cr+lf&gt; im done&lt;cr+lf&gt;  Simple! I can easily redirect its output to a file and I'm done. But the program I will have to deal with does it more like this: Program XYZ started..&lt;cr+lf&gt; processing 1&lt;cr&gt; processing 1 - part a&lt;cr&gt; processing 1 - part b&lt;cr&gt; processing 1 - part c&lt;cr&gt; processing 1 - part d&lt;cr&gt; &lt;cr+lf&gt; processing 2&lt;cr&gt; processing 2 - part a&lt;cr&gt; processing 2 - part b&lt;cr&gt; processing 2 - part c&lt;cr&gt; processing 2 - part d&lt;cr&gt; &lt;cr+lf&gt; processing 3&lt;cr+lf&gt; im done&lt;cr+lf&gt;  but much more intensive than I showed here. So it just not always overwrite status lines, but does it a lot while processing. So just redirecting or appending its output to a log file does not seem to make a lot of sense here, since it will just clutter the log file with millions of screen-updates that can not be viewed and understood that easily by humans. So my question is: is there a way or tool for programs that may behave like that to &quot;log&quot; or maybe &quot;screenshot every 30 seconds&quot; their output to a log file? This question was prompted by . Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone falling into the black hole reaches the event horizon, so could that person see the universe age by an infinite time?  To be more precise, suppose the observer starts falling from rest at time $t = 0$ and some initial distance $r &gt; r_s$. If we wait for some time $T$ then shine a light ray at the falling observer. Will the light ray always reach the falling observer before they cross the event horizon? If not, what is the formula for the longest time $T$ that we can wait and still be sure the ray will catch the observer? If $T$ is not bounded it implies that observer could indeed see the end of the universe.  I can think of a qualitative argument for an upper limit on $T$, but I'm not sure how sound my argument is. The proper time for the observer to fall to the event horizon is finite - call this $\tau$. The proper time for the light ray to reach the horizon is zero, therefore the light ray will reach the observer before they cross the event horizon only if $T &lt; \tau$. Hence $T$ is bounded and the observer won't see the end of the universe.  I think a more rigorous approach would be to determine the equations of motion (in the Schwarzschild coordinates) for the falling observer and the light ray, and then find the condition for the light to reach the falling observer at some distance $\epsilon$ from the event horizon. Then take the limit as $\epsilon \rightarrow 0$. In principle this seems straightforward, but in practice the algebra rapidly defeated me. Even for a light ray the radial distance:time equation isn't closed form (Wolfram claims it needs the $W$ function) and for the falling observer the calculation is even harder. How do you improve Drupal performance? When to spell out numbers Ubuntu 13.10 Macbook Air Mavericks Parallels 9 Black Screen I can install Ubuntu 13.10 in parallels ok and then log in.  Problem is Ubuntu does an update and I get black screen / desktop such that I can't see any app windows that I open.  I've tried a few of the other suggestions and they don't work for me. How to remove wine completely How can I remove the wine folder and all the applications in that folder?  I've tried via synaptic but it keeps showing up in the application menu. The RSA signature operation is basically the same as encrypting with the private key.  In particular, both operations use the same kind of keys.  Is it safe to use the same RSA keypair both for encryption / decryption and for signing / verification? Why do different humans look different? Although farmers appear to be able to tell their cows apart, cows look very much alike to me. And this similarity in appearance seems to be a general trait across the animal kingdom: one individual of one animal species looks much like another.  Why do human facial and body shapes vary so much?  I understand that human beings live in many different environments (e.g. hot and cold) and have adapted to these (e.g. through lighter or darker skin color), but there seems to be much variation that has no apparent evolutionary purpose. So does the difference have a purpose in itself? That is, did we evlove to vary in appearance, and what is the purpose of this variation? Splitting of prime ideals in algebraic extensions Google Chrome: Have different settings on different computers? What's the difference between a Long Term Support Release and a Normal Release? I have been reading about the new Salesforce async triggers. Currently, I tend to handle these sort of needs with a trigger that passes data to a 'Handler class' that would evaluate if a certain change has occurred. If it has then we pass those Ids to a queueable class for further processing.   What advantage do CDC and async triggers offer over using queueable or batch apex? I have a common scenario in app design, where I need to store an ordered list, and make the ordering easily accessible and adjustable via an application UI.    The ordering operations are simple and operate on only one item at a time - move to top, move to bottom, move up one position, or down one position.  These positioning operations may be interspersed in with typical add / edit / delete list operations.  For discussion, this is a single-user app and db store.  Because the objects can be highly complex, I'd like to avoid caching the entire list client-side, and tracking newly created objects in memory until a big save operation occurs.    I am using MS-SQL almost exclusively on these projects, and I'm wondering if there are db features, SQL features, or design patterns I should be using to better support the management of ordered lists.    My current approach is to use a DECIMAL column to store the list positions, which become fractional during the item move process.  Then I sort the list and re-generate integer positions to normalize list.  Following this operation, it's ready for another item move.   In an example implementation, I create a column named Seq for position tracking.  Once decimal place is enough for the .5 storage.   [Seq] [decimal](10, 1) NOT NULL   When an item is re-positioned in the app UI,    I UPDATE that record with new Seq value I retrieve the full table, sorted ascending by Seq and regenerate all Seq values in the table from a 1-based integer series   The new Seq value is easily calculated-    Move to top = 0 Move to bottom = MAX(Seq) + 1 Move up = subtract 1.5 from the current Seq value Move down = add 1.5 to the current Seq value   As lists get longer, updates get slower, since I'm doing N UPDATE statements, where N is the number of rows in the table, so it seems only suitable for small tables.    Is there some kind of in-built capability for managing an ordered list in SQL or MS-SQL? Is there a means to update multiple rows in one call?    A far more performant approach would be to allow more decimal places, and then position at the median of the two adjacent items, with no re-sequencing on the list.     Move to top = Min(Seq) - 1 Move to bottom = MAX(Seq) + 1 Move up = median of the 2 previous item Seq values Move down = median of the 2 following item Seq values   This approach only requires one SELECT (containing 2 rows max) and one UPDATE.    However with enough re-positions I imagine the field would run out of decimal places. For example, if I start with items at positions 10 and 11, and keep moving items down the list from position 9, they'd be given sequences of 10.5, then 10.25, then 10.125.  After 10 moves, the positions get lengthy... 10.0009765625.    UPDATE #1 - IMPROVED RE-SEQUENCING OF THE LIST  Regarding re-sequencing, I'm more caught up on row_number(), OVER, and WITH capabilities in MS-SQL.  It's nice to find that there's a much smoother way to re-sequence the list in a single UPDATE operation;  with OrderedItems as  (     select         ItemID,         Seq,         row_number() over (order by Seq asc) NewSeq     from          Items ) update OrderedItems set Seq = NewSeq Bash string range and replace To print part of the string, replace , with . I use command:  echo "${q:16:6}" | sed 's/,/./'   Is it possible to use something like:  echo "${q:16:6/,/.}"   because it does not work? UMP of product functor Eigenvalues of a matrix whose square equals its transpose Let $A$ be a $n\times n$ matrix with $A^2=A^t$. Show that every real eigen value of $A$ is either $ 0$ or $1$ Does the sign of $\Delta x$ matter in this time dilation calculation?