Pengwuino said:Exactly. The velocity of an object is simply the time-derivative of its position function.
jtbell said:##v_{yf}## isn't a constant, it's a variable, more specifically the dependent variable, a function of t. Written as functions, your two equations are
$$y(t) = y_i + v_{yi} t + \frac{1}{2}a_y t^2$$
$$v_y(t) = v_{yi} + a_y t$$
The first kinematics equation, also known as the position equation, describes the relationship between an object's initial position, final position, velocity, and time. The second kinematics equation, also known as the velocity equation, describes the relationship between an object's initial velocity, final velocity, acceleration, and time.
Yes, there is a connection between the two equations. The velocity equation can be derived from the position equation by taking the derivative with respect to time. This means that the two equations are related by the concept of calculus.
Yes, the kinematics equations are commonly used in physics and engineering to solve real-world problems involving motion. They can be used to calculate an object's position, velocity, acceleration, and time given certain variables.
While the kinematics equations are useful for solving many problems, they do have some limitations. They are based on the assumptions of constant acceleration and no external forces acting on the object, which may not always be true in real-life situations. Also, they are limited to one-dimensional motion and do not account for rotational or circular motion.
The kinematics equations can be applied to any type of motion as long as the assumptions of constant acceleration and no external forces hold true. This includes linear motion, projectile motion, and motion in a straight line with changing acceleration. However, they cannot be applied to rotational or circular motion.