About Velocity & Acceleration Vector Formula
The velocity vector formula describes the velocity of an object in terms of its speed and direction and is given by:
v = d/t
where v is the velocity vector, d is the displacement vector (the change in position of the object), and t is the time interval over which the displacement occurs.
The velocity vector can be expressed in terms of its components in a coordinate system, such as Cartesian coordinates. For example, in two-dimensional Cartesian coordinates, the velocity vector can be written as:
v = (vx, vy)
where vx is the x-component of the velocity vector, and vy is the y-component of the velocity vector.
The magnitude of the velocity vector, also known as the speed of the object, is given by:
|v| = sqrt(vx^2 + vy^2)
where sqrt is the square root function.
The direction of the velocity vector can be expressed in terms of the angle it makes with a reference axis, such as the positive x-axis in Cartesian coordinates. The angle can be found using trigonometry:
θ = atan(vy/vx)
where atan is the arctangent function, and θ is the angle between the velocity vector and the positive x-axis.