You're asking for the equations of motion that describe the relationship between velocity and time. There are three main equations of motion for constant acceleration, which can be used to find various quantities like displacement, velocity, and time. Here they are:

1. First Equation of Motion:

* Equation: v = u + at

* Description: This equation relates the final velocity (v) to the initial velocity (u), acceleration (a), and time (t). It states that the final velocity is equal to the initial velocity plus the product of acceleration and time.

2. Second Equation of Motion:

* Equation: s = ut + (1/2)at²

* Description: This equation relates the displacement (s) to the initial velocity (u), acceleration (a), and time (t). It states that the displacement is equal to the sum of the product of initial velocity and time, and half the product of acceleration and the square of time.

3. Third Equation of Motion:

* Equation: v² = u² + 2as

* Description: This equation relates the final velocity (v) to the initial velocity (u), acceleration (a), and displacement (s). It states that the square of the final velocity is equal to the square of the initial velocity plus twice the product of acceleration and displacement.

Key Points:

* These equations are only valid for motion with constant acceleration.

* Displacement is the change in position of an object.

* Velocity is the rate of change of displacement, and it has both magnitude (speed) and direction.

* Acceleration is the rate of change of velocity.

These three equations are crucial for understanding the relationship between velocity and time in a wide range of physics problems involving motion.