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of change of the distance travelled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalently a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which
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These common names correspond to terminology used in basic kinematics. By extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in
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that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another. For motion over a given interval of time, the displacement divided by the length of the time interval defines the
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in turn moves on its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a
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1384:{\displaystyle \mathbf {j} ={\frac {d\mathbf {a} }{dt}}={\frac {d^{2}\mathbf {v} }{dt^{2}}}={\frac {d^{3}\mathbf {s} }{dt^{3}}}}
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such as, for instance, a point fixed on the floor of the train station and the usual vertical and horizontal directions).
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of the net or total motion along a straight line from the initial position to the final position of the point
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of the object is the rate of change of the displacement as a function of time. The instantaneous
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1562:"3.1 Position, Displacement, and Average Velocity - University Physics Volume 1 | OpenStax"
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Vector relating the initial and the final positions of a moving point
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In considering motions of objects over time, the instantaneous
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1592:. National Aeronautics and Space Administration. 13 May 2021
1001:{\displaystyle s=x_{\textrm {f}}-x_{\textrm {i}}=\Delta {x}}
925:(resulting from the motion), that is, as the final position
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Moebs, William; Ling, Samuel J.; Sanny, Jeff (2016-09-19).
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order to accurately represent the displacement function as
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1614:(2001). "Ā§2.8 - The Derivative As A Function".
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1620:(2nd ed.). Brooks/Cole.
878:whose length is the shortest
439:Koopmanāvon Neumann mechanics
1066:{\displaystyle \mathbf {s} }
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304:Inertial frame of reference
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1540:The Physics Classroom
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68:
65:
59:
58:
53:
51:Common symbols
50:
47:
46:
43:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2818:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2783:
2781:
2764:
2755:
2750:
2747:
2739:
2734:
2731:
2729:
2726:
2724:
2715:
2710:
2707:
2699:
2694:
2691:
2689:
2686:
2685:
2682:
2673:
2668:
2663:
2658:
2653:
2648:
2645:
2643:
2634:
2629:
2624:
2623:
2617:
2614:
2612:
2609:
2607:
2598:
2593:
2588:
2583:
2578:
2573:
2570:
2568:
2556:
2551:
2546:
2541:
2538:
2536:
2533:
2532:
2529:
2525:
2513:
2505:
2502:
2500:
2491:
2485:
2480:
2475:
2472:
2470:
2467:
2465:
2461:
2449:
2441:
2438:
2436:
2432:
2423:
2418:
2413:
2408:
2405:
2403:
2379:
2376:
2364:
2361:
2358:
2357:
2354:
2352:
2350:
2341:
2336:
2333:
2330:
2328:
2325:
2322:
2318:
2314:
2309:
2307:
2302:
2297:
2294:
2291:
2290:
2287:
2278:
2277:
2271:
2268:
2266:
2263:
2261:
2256:
2251:
2248:
2246:
2243:
2242:
2239:
2237:
2228:
2227:
2221:
2218:
2216:
2211:
2207:
2204:
2202:
2200:
2195:
2190:
2187:
2185:
2182:
2181:
2178:
2176:
2167:
2166:
2160:
2155:
2150:
2149:angular speed
2147:
2145:
2141:
2135:
2134:
2128:
2121:
2116:
2109:
2104:
2100:
2097:
2092:
2087:
2081:
2076:
2073:
2071:
2066:
2061:
2056:
2051:
2048:
2046:
2042:
2036:
2031:
2027:
2024:
2023:
2019:
2011:
2007:
2005:
2000:
1999:
1993:
1988:
1983:
1980:
1978:
1975:
1973:
1968:
1963:
1960:
1958:
1954:
1948:
1942:
1936:
1931:
1925:
1920:
1917:
1915:
1912:
1911:
1908:
1906:
1904:
1899:
1894:
1891:
1888:
1886:
1884:
1879:
1874:
1871:
1869:
1864:
1859:
1856:
1853:
1852:
1848:
1844:
1841:
1837:
1834:
1831:
1828:
1825:
1822:
1819:
1818:
1808:
1803:
1799:
1796:
1789:
1784:
1782:
1777:
1775:
1770:
1769:
1766:
1754:
1751:
1749:
1746:
1744:
1741:
1738:
1734:
1731:
1728:
1724:
1721:
1719:
1716:
1715:
1712:
1705:
1704:Differentiate
1701:
1697:
1696:
1693:
1689:
1682:
1677:
1675:
1670:
1668:
1663:
1662:
1659:
1652:
1647:
1643:
1642:
1638:
1629:
1627:0-534-37718-1
1623:
1619:
1618:
1613:
1607:
1604:
1591:
1587:
1581:
1578:
1567:
1563:
1556:
1553:
1541:
1537:
1530:
1527:
1520:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1500:Motion vector
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1477:
1473:
1467:
1462:
1459:
1453:
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1434:
1429:
1428:
1422:
1418:
1414:
1406:
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1402:
1398:
1373:
1369:
1365:
1353:
1349:
1342:
1334:
1330:
1326:
1314:
1310:
1303:
1297:
1294:
1284:
1278:
1266:
1264:
1261:
1242:
1238:
1234:
1222:
1218:
1211:
1205:
1202:
1192:
1186:
1174:
1172:
1169:
1152:
1149:
1139:
1133:
1121:
1119:
1116:
1115:
1114:
1100:
1080:
1048:
1040:
1038:
1036:
1035:
1030:
1026:
1022:
1018:
1010:
1008:
994:
987:
976:
972:
961:
957:
954:
946:
938:
929:
924:
923:
914:
912:
910:
909:average speed
906:
901:
897:
893:
889:
885:
881:
877:
873:
869:
865:
853:
848:
846:
841:
839:
834:
833:
831:
830:
824:
814:
811:
806:
800:
799:
798:
797:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
670:
663:
662:
655:
651:
647:
643:
640:
639:
635:
632:
630:
627:
625:
622:
620:
617:
613:
610:
609:
608:
605:
603:
600:
598:
595:
593:
590:
589:
585:
580:
579:
571:
568:
566:
563:
559:
556:
554:
551:
550:
549:
546:
544:
541:
539:
536:
534:
529:
526:
522:
519:
518:
514:
511:
508:
504:
500:
499:
495:
492:
490:
487:
485:
482:
480:
475:
473:
470:
468:
465:
463:
460:
459:
452:
451:
440:
437:
435:
432:
430:
427:
425:
422:
420:
417:
415:
412:
411:
409:
408:
403:
400:
399:
394:
393:
387:
386:
378:
375:
373:
370:
368:
365:
363:
360:
358:
355:
353:
350:
348:
345:
343:
339:
337:
334:
332:
328:
326:
323:
320:
316:
312:
310:
307:
305:
302:
300:
297:
295:
292:
288:
285:
283:
280:
279:
278:
275:
273:
270:
268:
265:
263:
260:
258:
255:
254:
247:
246:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
200:
199:
192:
191:
185:
182:
180:
177:
175:
172:
171:
168:
164:
145:
142:
132:
126:
112:
111:
108:
104:
100:
99:
92:
89:
87:
83:
79:
77:
70:
66:
64:
60:
57:
54:
48:
41:
36:
31:
19:
2753:
2737:
2713:
2697:
2671:
2661:
2651:
2632:
2621:
2620:
2596:
2586:
2576:
2554:
2544:
2489:
2478:
2421:
2411:
2339:
2323:
2320:
2316:
2312:
2300:
2275:
2274:
2270:angular jerk
2254:
2225:
2224:
2193:
2189:acceleration
2164:
2163:
2153:
2132:
2131:
2119:
2107:
2090:
2079:
2064:
2054:
2034:
1997:
1996:
1986:
1966:
1953:displacement
1946:
1940:
1934:
1923:
1897:
1877:
1862:
1846:
1839:
1743:Acceleration
1723:Displacement
1722:
1615:
1606:
1594:. Retrieved
1589:
1580:
1569:. Retrieved
1566:openstax.org
1565:
1555:
1543:. Retrieved
1539:
1529:
1480:Affine space
1431:
1425:
1410:
1393:
1171:Acceleration
1050:
1032:
1028:
1021:displacement
1020:
1014:
936:
927:
920:
918:
872:displacement
871:
861:
652: /
648: /
646:displacement
644: /
505: /
467:Displacement
466:
405:
396:
390:Formulations
377:Virtual work
317: /
257:Acceleration
250:Fundamentals
90:
63:SI unit
55:
33:Displacement
2010:solid angle
1041:Derivatives
1019:, the term
915:Formulation
900:translation
788:von Neumann
455:Core topics
2780:Categories
2745:m s, N m s
2721:m s,
2667:Lagrangian
2592:Lagrangian
1832:Dimensions
1820:Dimensions
1688:Kinematics
1596:9 November
1571:2024-03-11
1521:References
1407:Discussion
1045:See also:
1017:rigid body
1011:Rigid body
945:difference
896:trajectory
723:d'Alembert
703:Maupertuis
666:Scientists
548:Rigid body
222:Kinematics
2761:ms,
2380:˙
2103:frequency
2030:frequency
1700:Integrate
1545:2 January
1421:time rate
1025:rotations
991:Δ
973:−
892:direction
868:mechanics
768:Liouville
650:frequency
570:Vibration
287:potential
212:Continuum
207:Celestial
184:Textbooks
86:Dimension
2705:m s, N s
2528:J s
2524:m s
2499:m s
2460:m s
2431:m s
2407:momentum
2060:velocity
1930:position
1919:distance
1873:absement
1798:SI units
1733:Velocity
1727:Distance
1718:Absement
1617:Calculus
1444:See also
1413:velocity
1118:Velocity
884:position
880:distance
864:geometry
823:Category
748:Hamilton
733:Lagrange
728:Clairaut
693:Horrocks
654:velocity
624:Pendulum
612:reactive
584:Rotation
553:dynamics
503:Inertial
489:Friction
372:Velocity
347:Momentum
227:Kinetics
217:Dynamics
195:Branches
179:Timeline
2733:rotatum
2512:actergy
2448:actergy
2417:impulse
2337::
2088::
2018:rad, sr
783:Koopman
743:Poisson
738:Laplace
683:Huygens
678:Galileo
523: (
462:Damping
315:Inertia
309:Impulse
282:kinetic
232:Statics
202:Applied
174:History
2791:Length
2647:energy
2628:moment
2616:torque
2572:energy
2550:weight
2522:
2504:action
2497:
2458:
2440:action
2429:
2400:
2347:
2319:ā© = ā
2283:
2234:
2173:
1624:
1401:jounce
888:motion
876:vector
821:
773:Appell
758:Cauchy
753:Jacobi
698:Halley
688:Newton
673:Kepler
525:linear
521:Motion
367:Torque
342:Moment
277:Energy
267:Couple
2749:power
2709:power
2679:m s,
2640:m s,
2604:m s,
2565:m s,
2540:force
2050:speed
1982:angle
1737:Speed
1417:speed
874:is a
778:Gibbs
763:Routh
718:Euler
357:Speed
352:Space
294:Force
67:metre
2693:yank
2657:work
2582:work
2296:mass
2250:jerk
1962:area
1893:time
1858:time
1748:Jerk
1622:ISBN
1598:2023
1547:2012
1263:Jerk
870:, a
866:and
362:Time
325:Mass
2727:MLT
2642:N m
2610:MLT
2563:kg
2468:MLT
2464:J s
2435:N s
2281:rad
2259:m s
2232:rad
2199:m s
2171:rad
2095:m s
2070:m s
2004:rad
1883:m s
862:In
72:In
2782::
2759:kg
2751::
2743:kg
2735::
2719:kg
2711::
2703:kg
2695::
2687:MT
2677:kg
2669::
2665:,
2659::
2655:,
2649::
2638:kg
2630::
2626:,
2618::
2602:kg
2594::
2590:,
2584::
2580:,
2574::
2552::
2548:,
2542::
2534:MT
2526:,
2520:kg
2514::
2510:,
2508:š®
2506::
2495:kg
2486::
2482:,
2476::
2462:,
2456:kg
2450::
2446:,
2444:š®
2442::
2433:,
2427:kg
2419::
2415:,
2409::
2398:kg
2365::
2359:MT
2345:kg
2331:ML
2306:kg
2298::
2272::
2252::
2222::
2191::
2161::
2157:,
2151::
2144:Hz
2142:,
2129::
2124:,
2117::
2112:,
2105::
2077::
2062::
2058:,
2052::
2045:Hz
2043:,
2032::
2012::
1994::
1990:,
1984::
1964::
1951:,
1944:,
1938:,
1932::
1927:,
1921::
1895::
1875::
1860::
1702:ā¦
1698:ā
1588:.
1564:.
1538:.
1403:.
1037:.
2763:W
2754:P
2738:P
2723:W
2714:P
2698:Y
2681:J
2672:L
2662:W
2652:E
2633:M
2622:Ļ
2606:J
2597:L
2587:W
2577:E
2567:N
2558:g
2555:F
2545:F
2516:āµ
2490:L
2488:Ī
2479:L
2452:āµ
2422:J
2412:p
2402:s
2377:m
2349:m
2340:I
2324:x
2321:m
2317:x
2315:āØ
2313:M
2301:m
2292:M
2285:s
2276:Ī¶
2264:T
2255:j
2244:T
2236:s
2226:Ī±
2215:s
2205:T
2194:a
2183:T
2175:s
2165:Ļ
2154:Ļ
2140:s
2133:n
2120:n
2108:f
2098:T
2091:h
2083:,
2080:Ī½
2065:v
2055:v
2041:s
2035:f
2025:T
2014:Ī©
1998:Īø
1987:Īø
1976:1
1972:m
1967:A
1957:m
1947:x
1941:s
1935:r
1924:d
1913:1
1903:s
1898:t
1889:T
1878:A
1868:s
1863:t
1854:T
1847:Īø
1840:Īø
1835:1
1829:L
1826:L
1823:1
1787:e
1780:t
1773:v
1739:)
1735:(
1729:)
1725:(
1706:ā
1680:e
1673:t
1666:v
1630:.
1600:.
1574:.
1549:.
1374:3
1370:t
1366:d
1360:s
1354:3
1350:d
1343:=
1335:2
1331:t
1327:d
1321:v
1315:2
1311:d
1304:=
1298:t
1295:d
1289:a
1285:d
1279:=
1275:j
1243:2
1239:t
1235:d
1229:s
1223:2
1219:d
1212:=
1206:t
1203:d
1197:v
1193:d
1187:=
1183:a
1153:t
1150:d
1144:s
1140:d
1134:=
1130:v
1101:t
1081:t
1060:s
995:x
988:=
982:i
977:x
967:f
962:x
958:=
955:s
940:i
937:x
931:f
928:x
851:e
844:t
837:v
527:)
146:t
143:d
137:p
133:d
127:=
122:F
91:L
80:m
56:d
20:)
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