Lecture 1 | 1D Kinematics of Constant Acceleration

1D Kinematics

Lecture 1 | 1D Kinematics of Constant Acceleration

1D Kinematics

Kinematics is the study of the motion of objects. One dimensional (1-D) kinematics studies the motion of objects moving along a straight line with constant acceleration. The major goal is to develop the ability to mathematically model the motion by applying the kinematic equations for constant acceleration.

OpenStax AP Physics Chapter 2: One-Dimensional Kinematics (Physics Concept Trailer™)

Pre-lecture Study Resources

Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.

1-D Kinematics | Position and Displacement

Just as understanding motion can be accomplished through the aid of plots, we also use a purely mathematical representation to predict the motion of an object. Here we are going to focus on the mathematical representation of motion. Given information of position, acceleration and velocity as functions of time, we use kinematics to determine the values such as average speed, final or initial positions, time of travel and many others. Here we introduce kinematics using motion in a straight line, such as a car, train, rocket, etc. Pivotal to kinematics are the Kinematic Equations for Constant Acceleration:

$Position_{\: final} = Position_{\: initial} + Velocity_{\: initial}*Change \: in \: Time + \frac{1}{2} Acceleration * (Change \: in \: Time)^2$

$Velocity_{\: final} = Velocity_{\: initial} + Acceleration * (Change \: in \: Time)$

which can be more concisely written as

(i) $x_f = x_i+v_i \Delta t + \frac{1}{2} a \Delta t ^2$

(ii) $v_f = v_i + a \Delta t$

By solving the velocity equation for time, and substituting that into the position equation, we arrive at

$x_f = v_i (\frac{v_f - v_i}{a})+\frac{1}{2} a (\frac{v_f - v_i}{a})^2$

which can be rearranged to our third kinematic equation

(iii) $v_f^2 =v_i^2+2a\Delta x$

FreeFall | An object traveling along a vertical line (either straight up or straight down), that is only under the influence of gravity, is considered to be in freefall. It has a constant acceleration that points downward at all times. The magnitude of the acceleration is 9.8 m/s².