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Related Concept Videos

Distance Problem01:29

Distance Problem

When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
Kinematic Equations - II01:17

Kinematic Equations - II

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.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Average and Instantaneous Velocity Vectors01:12

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object is (its position) during its motion, but also how fast it’s moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position, a particular time is assigned. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity v. This...
Average Velocity01:12

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position of the object during its motion, but also how fast it is moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position xi, we assign a particular time ti. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity. This...
Relative Velocity in One Dimension01:10

Relative Velocity in One Dimension

The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...
Velocity and Position by Graphical Method01:34

Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to calculate...

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Related Experiment Video

Updated: Jun 2, 2026

Comparative Analysis of Lower Limb Kinematics between the Initial and Terminal Phase of 5km Treadmill Running
08:26

Comparative Analysis of Lower Limb Kinematics between the Initial and Terminal Phase of 5km Treadmill Running

Published on: July 17, 2020

Relationship between speed and time in running.

D W Hill1, J L Vingren, F Y Nakamura

  • 1University of North Texas, Kinesiology, Health Promotion and Recreation, Denton 76203, USA. david.hill@unt.edu

International Journal of Sports Medicine
|May 13, 2011
PubMed
Summary
This summary is machine-generated.

The 2-parameter hyperbolic model accurately describes treadmill running speed and time to exhaustion, providing reliable critical speed and anaerobic distance capacity values. Other models were less precise.

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Related Experiment Videos

Last Updated: Jun 2, 2026

Comparative Analysis of Lower Limb Kinematics between the Initial and Terminal Phase of 5km Treadmill Running
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Published on: July 17, 2020

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Area of Science:

  • Exercise Physiology
  • Biomechanical Modeling

Background:

  • Understanding the relationship between exercise intensity and duration is crucial for performance analysis.
  • Mathematical models are used to predict physiological limits during exercise.

Purpose of the Study:

  • To evaluate different mathematical models for describing the relationship between treadmill running speed and time to exhaustion.
  • To identify the most reliable model for determining critical speed (S (critical)) and anaerobic distance capacity (ADC).

Main Methods:

  • 35 university students completed constant-speed treadmill tests (3-10 min).
  • Speed and exhaustion time data were fitted using three models: 2-parameter hyperbolic, 3-parameter hyperbolic, and a hybrid model.
  • Model performance was assessed based on parameter estimates and statistical certainty.

Main Results:

  • The 2-parameter hyperbolic model yielded reliable S (critical) and ADC values with high statistical certainty.
  • 3-parameter models produced unrealistic parameter estimates with significant uncertainty.
  • The 2-parameter model offered a parsimonious description of speed-time to fatigue data.

Conclusions:

  • The 2-parameter hyperbolic model is preferred for describing the speed-time to exhaustion relationship in this exercise duration range.
  • This model provides physiologically significant parameters with excellent confidence.
  • It offers a statistically sound and practical approach to analyzing endurance performance.