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Kinematic Equations - I01:26

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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
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Kinematic Equations - II01:17

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
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In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
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Related Experiment Video

Updated: Feb 11, 2026

Lower-Limb Biomechanical Characteristics Associated with Unplanned Gait Termination Under Different Walking Speeds
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Kinematic patterns while walking on a slope at different speeds.

A H Dewolf1, Y Ivanenko2, K E Zelik2,3,4,5

  • 1Laboratory of Biomechanics and Physiology of Locomotion, Institute of NeuroScience, Université Catholique de Louvain , Louvain-la-Neuve , Belgium.

Journal of Applied Physiology (Bethesda, Md. : 1985)
|April 27, 2018
PubMed
Summary
This summary is machine-generated.

Lower limb coordination during walking changes with terrain slope and speed. At slow speeds, limb length and orientation adjust for slope; at faster speeds, limb orientation becomes the primary adjustment.

Keywords:
intersegmental coordinationkinematicsplanar covariationslopewalking

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Area of Science:

  • Biomechanics
  • Human locomotion
  • Kinematics

Background:

  • Lower limb segment angles (thigh, shank, foot) exhibit planar covariation during walking.
  • This coordination pattern reflects how different body segments move together.

Purpose of the Study:

  • To investigate how lower limb intersegmental coordination changes with terrain slope and walking speed.
  • To determine the relationship between kinematic patterns and the body's center of mass trajectory.

Main Methods:

  • Ten subjects walked on an inclined treadmill at various slopes (-9° to +9°) and speeds (0.56 to 2.22 m/s).
  • Principal component analysis (PCA) was used to analyze the covariance of thigh, shank, and foot elevation angles.

Main Results:

  • Planar covariation of limb segments was maintained across all conditions (>99% variance explained by two principal components).
  • At slow speeds, changes in coordination with slope involved primarily the plane's orientation and limb length (PC2*), with less change in limb orientation (PC1*).
  • At faster speeds, changes in coordination with slope were mainly driven by limb orientation (PC1*), with minimal changes in plane orientation and limb length (PC2*).

Conclusions:

  • Lower limb kinematic patterns are significantly influenced by both terrain slope and walking speed.
  • Slope-dependent kinematic modifications are speed-dependent, affecting body center of mass trajectory.
  • At slow speeds, vertical displacement is linked to limb length and orientation; at high speeds, it's primarily limb orientation.