Tru Physics

Velocity

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Velocity is a vector quantity that describes the rate at which an object changes its position. It is defined as the displacement of an object per unit of time and has both magnitude and direction.

Velocity is often measured in meters per second (m/s), but other units such as feet per second (ft/s) or miles per hour (mph) can also be used.

Average Velocity

The average velocity is defined as the displacement of an object divided by the time interval during which the displacement occurred. It is a vector quantity, and the direction of the average velocity is in the direction of displacement.

\vec{v}_{avg} = \dfrac{\Delta x}{\Delta t}

where \vec{v}_{avg} is the average velocity, \Delta x is the displacement of the object, and \Delta t is the time interval over which the displacement occurs.

Instantaneous Velocity

Instantaneous velocity is the velocity of an object at a particular point in time. It can be found by taking the limit of the displacement of the object over a very small time interval, approaching zero.

\vec{v} = \lim_{\Delta t \to 0} \dfrac{\Delta x}{\Delta t} = \dfrac{\mathrm{d} x}{\mathrm{d} t}

where \vec{v} is the instantaneous velocity, \Delta x is the displacement of the object over a small time interval \Delta t, and \frac{\mathrm{d}}{\mathrm{d} t} is the derivative with respect to time.

In 1-, 2-, and 3-Dimensions

In one-dimensional motion, the velocity of an object can be described by a single number that indicates both the magnitude and direction of the velocity. For example, if an object is moving to the right at a speed of 10 m/s, its velocity is +10 m/s. If the object is moving to the left at the same speed, its velocity is -10 m/s.

In two or three-dimensional motion, the velocity of an object can be described by a vector that specifies both the magnitude and direction of the velocity. The velocity vector is defined as:

\vec{v} = \dfrac{\Delta \vec{r}}{\Delta t} = \dfrac{\mathrm{d} \vec{r}}{\mathrm{d} t}

where v is the velocity vector, \Delta \vec{r} is the displacement vector, \Delta t is the time interval over which the displacement occurs, and \frac{\mathrm{d}}{\mathrm{d}t} is the derivative with respect to time.

Speed, Velocity, and Acceleration

The magnitude of the velocity vector is the speed of the object, and the direction of the velocity vector is the direction of the object’s motion.

On the other hand, the acceleration vector is the time derivative of the velocity vector, meaning that it is the change in velocity over time. The acceleration vector can be used to describe the rate at which an object’s velocity is changing, including the direction of the change in velocity.

Displacement is related to velocity in much the same way that velocity is related to acceleration.

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  1. Acceleration – Tru Physics

    […] is one of the most fundamental concepts in physics and is a measure of how an object’s velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. It is […]

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