Displacement (geometry)

Displacement versus distance travelled along a path

In

direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation 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.^[2]

A displacement may also be described as a

relative position (resulting from the motion), that is, as the final position

x f

of a point relative to its initial position

x i

. The corresponding displacement vector can be defined as the difference

between the final and initial positions:

s=x_{\textrm {f}}-x_{\textrm {i}}=\Delta {x}

In considering motions of objects over time, the instantaneous

absolute velocity, which is computed with respect to a point and coordinate axes which are considered to be at rest (a inertial frame of reference

such as, for instance, a point fixed on the floor of the train station and the usual vertical and horizontal directions).

For motion over a given interval of time, the displacement divided by the length of the time interval defines the

average speed

, which is a scalar quantity.

Rigid body

In dealing with the motion of a rigid body, the term displacement may also include the rotations of the body. In this case, the displacement of a particle of the body is called linear displacement (displacement along a line), while the rotation of the body is called angular displacement.^[3]

Derivatives

For a position vector $\mathbf {s}$ that is a function of time $t$ , the derivatives can be computed with respect to $t$ . The first two derivatives are frequently encountered in physics.

Velocity: $\mathbf {v} ={\frac {d\mathbf {s} }{\mathrm {d} t}}$
Acceleration: $\mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {s} }{dt^{2}}}$
Jerk: $\mathbf {j} ={\frac {d\mathbf {a} }{dt}}={\frac {d^{2}\mathbf {v} }{dt^{2}}}={\frac {d^{3}\mathbf {s} }{dt^{3}}}$

These common names correspond to terminology used in basic kinematics.

jounce

.

References

^ Tom Henderson. "Describing Motion with Words". The Physics Classroom. Retrieved 2 January 2012.
^ Moebs, William; Ling, Samuel J.; Sanny, Jeff (2016-09-19). "3.1 Position, Displacement, and Average Velocity - University Physics Volume 1 | OpenStax". openstax.org. Retrieved 2024-03-11.
^ "Angular Displacement, Velocity, Acceleration". NASA Glenn Research Center. National Aeronautics and Space Administration. 13 May 2021. Retrieved 9 November 2023.
ISBN 0-534-37718-1
.

External links

Media related to Displacement vector at Wikimedia Commons

v
t
e
Kinematics

← Integrate … Differentiate →

Absement

Displacement (Distance)

Velocity (Speed)

Acceleration

Jerk

Higher derivatives

v
t
e
Classical mechanics SI units

Linear/translational quantities Angular/rotational quantities

Dimensions 1 L L² Dimensions 1 $θ$ $θ$ ²

T time: $t$
s
m s
T time: $t$
s

1
displacement
m
area: $A$
m² 1 angle: $θ$ , angular displacement: $θ$
rad solid angle: $Ω$
rad², sr

T⁻¹ frequency: $f$
s⁻¹, Hz speed: $v$ , velocity: $v$
m s⁻¹
kinematic viscosity: $ν$ ,
specific angular momentum
: $h$
m² s⁻¹ T⁻¹
rotational velocity: $n$
s⁻¹, Hz

angular speed: $ω$ , angular velocity: $ω$
rad s⁻¹

T⁻² acceleration: $a$
m s⁻² T⁻²
s⁻²

rad s⁻²

T⁻³ jerk: $j$
m s⁻³ T⁻³ angular jerk: $ζ$
rad s⁻³

M mass: $m$
kg weighted position: $M ⟨ x ⟩ = \sum m x$ ML²
kg m²

MT⁻¹ Mass flow rate: ${\dot {m}}$
kg s⁻¹

N s

kg m² s⁻¹, J s
ML²T⁻¹
kg m² s⁻¹

kg m² s⁻¹, J s

MT⁻² force: $F$ , weight: $F g$
kg m s⁻², N energy: $E$ , work: $W$ , Lagrangian: $L$
kg m² s⁻², J ML²T⁻² torque: $τ$ , moment: $M$
kg m² s⁻², N m energy: $E$ , work: $W$ , Lagrangian: $L$
kg m² s⁻², J

MT⁻³
yank
: $Y$
kg m s⁻³, N s⁻¹ power: $P$
kg m² s⁻³, W ML²T⁻³
rotatum
: $P$
kg m² s⁻³, N m s⁻¹ power: $P$
kg m²s⁻³, W

Retrieved from "https://en.wikipedia.org/w/index.php?title=Displacement_(geometry)&oldid=1215432780"

[1] Tom Henderson. "Describing Motion with Words". The Physics Classroom. Retrieved 2 January 2012.

[2] Moebs, William; Ling, Samuel J.; Sanny, Jeff (2016-09-19). "3.1 Position, Displacement, and Average Velocity - University Physics Volume 1 | OpenStax". openstax.org. Retrieved 2024-03-11.

[3] "Angular Displacement, Velocity, Acceleration". NASA Glenn Research Center. National Aeronautics and Space Administration. 13 May 2021. Retrieved 9 November 2023.

[stewart-4] ISBN 0-534-37718-1
.

[2]

[3]

Rigid body

Derivatives

See also

References

External links