Understanding Vector Velocity and Their Components

Introduction

The location vector of a particle at time t is represented by the variational vector-valued function r(t).

A complicated concept known as “velocity vectors” is often employed in investigations to identify and address scientific issues. This phrase comprises the phrases “velocity” and “vector.” These two terms each have a distinct meaning. Simply put, velocity is the rate at which movement changes. However, a vector is a physical quantity that has both size and direction. A line with an arrowhead would be thought to be a vector’s graphical representation. Here, the bolt depicts the direction of the vector, and the length of the line formed across the actual quantity represents the magnitude of the vector.

What Is the Definition of a Velocity Vector?

Consider a body travelling in a horizontal path OX at a constant velocity V.

Let O represent the measurement site, and let t be the time at O.

Let t1 and t2 be the positions of the item at coordinates A and B, respectively.

OA−→−OA→\\overrightarrow{OA} = x1→x1→\\overrightarrow{x_1} and OB−→−OB→\\overrightarrow{OB} = x2→x2→\\overrightarrow{x_2}. Then, the body is displaced in the time interval of –(t2 – t1) = AB−→−AB→\\overrightarrow{AB} – OA−→−OA→\\overrightarrow{OA} = x2→x2→\\overrightarrow{x_2} – x1→x1→\\overrightarrow{x_1}Hence, Velocity =  Displacement/Time interval

The body is then propelled forward in time by (t2 – t1), which equals AB (AB overrightarrow).OA (overrightarrow) = x2 (overrightarrow) x1 (overrightarrow)

Velocity is thus defined as displacement over time.

Thus, the velocity vector, V, equals (x2 x 1)t2 t1.

 Explanation

• The word “velocity vectors” is created by fusing the concepts of “velocity” and “vectors.” We refer to “velocity” as the pace at which a displacement changes. Physical quantities with both a magnitude and a direction are called vectors. In graphics, a line with an arrowhead on it represents a velocity vector. To simplify the computations, we divided the diagonal velocity V into horizontal vx and vertical vy components in this manner.
• Two-dimensional motion is undoubtedly more complicated than one-dimensional motion since velocities might point in diagonal directions. To further understand this concept, imagine a baseball moving horizontally and vertically simultaneously while having a diagonal velocity of v. To simplify our computations, we split this vector velocity component into horizontal (vx) and vertical (vy) components.
• By dividing the diagonal velocity v into the horizontal vx and vertical vy components, we can deal with each direction independently. This way of breaking up the vectors into elements works even when the vector is anything other than velocities, like force or momentum.

Components of Vector

Before we start with velocity vectors, let’s review the basic trigonometric rules:

The hypotenuse, opposite, adjacent, and one of the angles may all be connected using the relationship shown below.

Rules of Trigonometry

The total velocity vectors and their components combine to produce a right-angle triangle when the diagonal vector is divided into two perpendicular halves. As a consequence, velocity vectors are subject to the same trigonometric rules.

Applications

Following are a few uses for velocity vectors:

• A velocity vector shows how quickly an object’s location changes.
• A velocity vector’s magnitude represents an object’s speed, while its vector direction represents its direction.
• Using vector addition concepts, velocity vectors can be added to or subtracted from.

Important Information

• A velocity vector shows how quickly an object’s location changes.
• While the vector direction designates an item’s direction, the velocity vector’s size indicates the activity’s speed.
• Divide the distance by the time it takes to go that distance, multiply by the direction, and that is your velocity.
• A negative velocity item moves in the opposite direction when an object’s speed decreases; its acceleration vector shifts to correspond with the change in motion.

Managing Velocity as a Vector

Due to the fact that velocity is a vector, it has a magnitude and a direction. Assume you are in a vehicle moving east at 88 metres per second when you start to accelerate north for 10.0 seconds at 5.0 metres per second. What’s the fastest you can go?

You could believe that by using this equation, you can get the solution:

Vf = Vo + Ax + T

However, this is a scalar equation, not a vector equation (the magnitude of a vector is a scalar). Since this acceleration and the beginning speed are moving in opposite directions, this scalar equation cannot be used in this situation. Actually, because speed is a scalar, velocity must be used instead of speed when thinking about it.

This equation also exists as a vector equation:

Vf = Vo + Ax + T

In this case, everything is a vector except for time, so take note that now the speeds are velocities (speed is the magnitude of a velocity vector), not speed (which is always a scalar). Due to the fact that vectors can handle addition in more than one dimension and not simply a straight line, this alteration implies that the addition you execute in this formula is vector addition.

Recommended Articles:

Venus – Characteristics, Geology and Facts
Volcano Eruption: The Science Behind Volcanic Eruptions
What is Vt Graphs? Definition, Case and Formula
Wave Function – Definition, Equation, Function and Mechanics
Wave Theory Of Light – History, Theory, Principle & Types