1D Kinematics

change in position. It can be positive, negative, or zero.

Ratio of the displacement to the elapsed time interval.

uses total distance traveled, not displacement.

Derivative of position with respect to time.

Ratio of the change in velocity to the elapsed time interval.

Derivative of velocity with respect to time, equivalent to the second derivative of position.

In uniform rectilinear motion, position varies linearly with time at constant velocity.

• $v$ constant and $a=0$.

In uniformly accelerated rectilinear motion, velocity varies linearly with time.

• constant acceleration.

Position in rectilinear motion with constant acceleration.

explicitly eliminates time from the equations of uniformly accelerated motion.

With constant acceleration, the displacement is the product of the average velocity and the time.

• constant acceleration.

Velocity is obtained by integrating the acceleration from an initial instant.

Position is obtained by integrating the velocity from an initial instant.

Vertical velocity in free fall with downward acceleration of magnitude g.

• $y$-axis positive upward and negligible air resistance.

Vertical position in free fall with downward acceleration of magnitude g.

Relation between velocity and vertical displacement in free fall, without explicit time.

Maximum height reached in a vertical throw relative to the launch point.

• strictly vertical launch; $v_y=0$ at maximum height; negligible air resistance.

Time elapsed until the maximum height is reached in a vertical throw.

Round-trip time back to the same height in a vertical throw.

• the object returns to the same height from which it was launched.