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General Equations of Kinematics

From the instantaneous situation, similar equations of 1D kinematics can be used to calculate the unknown quantity from the known quantities for 1D motion.

Equations of  1D Kinematics

Acceleration as a function of time t

The motion of an object is described with respect to time. From the Instantaneous Situations, general equations of 1D kinematics are derived to calculate unknown quantity for the motion of an object as following.

For uniform motion where a=0, imply.

For uniformly accelerated motion where a=constant, imply.

Acceleration as a function of position

When position is a function of time, the motion of an object can also be described with respect to position, if time t can also be expressed as a continuous function of position x. From the instantaneous situations, both the instantaneous velocity and instantaneous acceleration with respect to the time t are also related to same position x as position x is a function of time t.

For uniform motion where a=0, imply.

For uniformly accelerated motion where a=constant, imply.

Acceleration as a function of velocity

When velocity is a function of time, the motion of an object can also be described with respect to velocity, if time t can also be expressed as a continuous function of velocity v. From the instantaneous situations, both the position and instantaneous acceleration with respect to the time t are also related to same velocity v as velocity x is a function of time t.

For uniform motion where a=0, imply.

For uniformly accelerated motion where a=constant, imply.

General Equations of  1D Kinematics

General equations of 1D kinematics are.