The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...

Enzyme kinetics studies the rates of biochemical reactions. Scientists monitor the reaction rates for a particular enzymatic reaction at various substrate concentrations. Additional trials with inhibitors or other molecules that affect the reaction rate may also be performed.
The experimenter can then plot the initial reaction rate or velocity (Vo) of a given trial against the substrate concentration ([S]) to obtain a graph of the reaction properties. For many enzymatic reactions involving a...

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:

Enzymes speed up reactions by lowering the activation energy of the reactants. The speed at which the enzyme turns reactants into products is called the rate of reaction. Several factors impact the rate of reaction, including the number of available reactants. Enzyme kinetics is the study of how an enzyme changes the rate of a reaction.
Scientists typically study enzyme kinetics with a fixed amount of enzyme in the controlled environment of a test tube. When more reactant, or substrate, is...

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...