Motion in the plane

This part defines two things that every later part of the course uses: a way to state the Position of an object, and a way to predict its later position and Velocity. Velocity and Acceleration are time derivatives of position. So this part defines position first.

Part 1 of 22 chapters35–45 min8 numbered equations2 knowledge checks

1. Position and Coordinate Systems

   Locate a moving point in the plane in Cartesian and polar coordinates, and read velocity and acceleration off position as time derivatives.

   20–30 min7 equations1 checkdraft

2. Velocity Under Constant Acceleration

   Predict an object's velocity at any later time from its initial velocity and a constant acceleration.

   15 min1 equation1 checkdraft

The argument

1. Cartesian or polar coordinates state the position of a point in the plane
2. Velocity and acceleration are the first and the second time derivative of position
3. For a constant acceleration, integration gives the velocity and the position in closed form

After this part you can

• Given a point in the plane, convert between Cartesian and polar coordinates, and identify velocity and acceleration as the first and second time derivatives of position.
• Given an initial velocity and a constant acceleration, compute the velocity at a later time.

Leads to

• Projectile motion