Physics › Kinematics ›

# velocity

Average and instantaneous velocity of an object

Controller: **CodeCogs**

## Dependents

## Interface

C++

Excel

## Overview

This module computes the average and instantaneous velocity of a moving object at given moments of time.### Authors

*Lucian Bentea (July 2007)*

## Velocity Avg

doublevelocity_avg( | double | xf | |

double | tf | ||

double | x0` = 0` | ||

double | t0` = 0` | )[inline] |

### Example 1

#include <codecogs/physics/kinematics/velocity.h> #include <iostream> int main() { // final position and time double x = 100, t = 15.7; std::cout << std::endl; std::cout << " Final position = " << x << " m" << std::endl; std::cout << " Time spent = " << t << " s" << std::endl; std::cout << std::endl; // assuming initial position and initial time are null, // display the average velocity of the object std::cout << "Average velocity = " << Physics::Kinematics::velocity_avg(x, t); std::cout << " m/s" << std::endl; return 0; }

**Output**Final position = 100 m Time spent = 15.7 s Average velocity = 6.36943 m/s

### Parameters

xf final position on the axis (meters) tf final time (seconds) [needs to be different from t0] x0 Default value = 0 t0 Default value = 0

### Returns

- the average velocity of the moving object (meters per second)

##### Source Code

This module is private, for owner's use only.

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## Velocity Ins

doublevelocity_ins( | double | (*x)(double)[function pointer] | |

double | t | ||

double | eps` = 1E-6` | )[inline] |

*t*, given a function

*x*which determines the position of the object at any moment of time. It is based on the fact that the instantaneous velocity function is given by the derivative of the position function with respect to time, i.e. Since this function uses numerical differentiation to compute the above derivative, an optional parameter

*eps*is available to specify the precision of numerical computations.

### Example 2

#include <codecogs/physics/kinematics/velocity.h> #include <iostream> // function defining the position at any moment of time t; // in this case pos(t) = t^3 double pos(double t) { return t*t*t; } int main() { // time at which to calculate instantaneous velocity double t = 11.43; std::cout << std::endl; std::cout << "Position = " << pos(t); std::cout << " m" << std::endl; std::cout << " Time = " << t; std::cout << " s" << std::endl; std::cout << std::endl; // display instantaneous velocity at time t std::cout << "Instantaneous velocity = " << Physics::Kinematics::velocity_ins(space, t); std::cout << " m/s" << std::endl; return 0; }

**Output**Position = 1493.27 m Time = 11.43 s Instantaneous velocity = 391.935 m/s

### Parameters

x function defining the position of the object at any moment of time (meters) t the moment of time at which the instantaneous velocity is to be evaluated (seconds) eps Default value = 1E-6

### Returns

- the instantaneous velocity of the object at time
*t*(meters per second)

##### Source Code

This module is private, for owner's use only.

Not a member, then Register with CodeCogs. Already a Member, then Login.

## Velocity Ins

std::vector<double>velocity_ins( | double | (*x)(double)[function pointer] | |

std::vector<double>& | t | ||

double | eps` = 1E-6` | )[inline] |

### Example 3

#include <codecogs/physics/kinematics/velocity.h> #include <iostream> // function defining the position at any moment of time t; // in this case pos(t) = t^3 double pos(double t) { return t*t*t; } int main() { // moments of time at which to evaluate // the instantaneous velocity of the object double t[10] = { 11.40, 11.41, 11.42, 11.43, 11.44, 11.45, 11.46, 11.47, 11.48, 11.49 }; // compute the instantaneous velocities std::vector<double> time(t, t+10), velocities = Physics::Kinematics::velocity_ins(distance, time); // display the time, the position // and the instantaneous velocities std::cout << std::endl; for (int i = 0; i < 10; i++) { std::cout << "Time = " << time[i] << " s"; std::cout << "\tPosition = " << pos(time[i]) << " m"; std::cout << "\tVelocity = " << velocities[i] << " m/s"; std::cout << std::endl; } return 0; }

**Output**Time = 11.4 s Position = 1481.54 m Velocity = 389.88 m/s Time = 11.41 s Position = 1485.45 m Velocity = 390.564 m/s Time = 11.42 s Position = 1489.36 m Velocity = 391.249 m/s Time = 11.43 s Position = 1493.27 m Velocity = 391.935 m/s Time = 11.44 s Position = 1497.19 m Velocity = 392.621 m/s Time = 11.45 s Position = 1501.12 m Velocity = 393.307 m/s Time = 11.46 s Position = 1505.06 m Velocity = 393.995 m/s Time = 11.47 s Position = 1509 m Velocity = 394.683 m/s Time = 11.48 s Position = 1512.95 m Velocity = 395.371 m/s Time = 11.49 s Position = 1516.91 m Velocity = 396.06 m/s

### Parameters

x function defining the position of the object at any moment of time (meters) t array containing the moments of time at which the instantaneous velocities should be evaluated (seconds) eps Default value = 1E-6

### Returns

- array containing the instantaneous velocities of the object at moments of time given by
*t*(meters per second)

##### Source Code

This module is private, for owner's use only.

Not a member, then Register with CodeCogs. Already a Member, then Login.