Introduction to Mechanics: Kinematics

Explore kinematics, the study of motion, and the differences between perception, distance traveled, and displacement. Learn speed, velocity, position, and average versus instantaneous acceleration with graphical representations.

Define position, distance traveled, and displacement, and show that displacement is independent of the path, based on initial and final positions.

Explain how velocity is a vector with direction and speed is its magnitude, which is always positive. Compare average versus instantaneous values using displacement over time and distance over time.

Compute the average velocity as the slope between two points on a position-time graph, and instantaneous velocity as the tangent slope, with examples and turning points.

Explore how acceleration, including average and instantaneous forms, describes velocity changes and relates to the slope of the velocity-time graph, with concavity and point-of-inflection signaling acceleration changes.

Relate position, velocity, and acceleration using calculus, linking instantaneous velocity to the limit of delta x over delta t and acceleration to the second derivative of position.

Derive the four kinematic equations for motion under constant acceleration by linking acceleration, velocity, and position, and illustrate with velocity and displacement graphs.

This lecture covers three problems under constant acceleration, solving with the four kinematic equations: stopping from 40 m/s in 30 m, traveling 4 s at 2 m/s^2, and a catch-up.

Observe free fall under gravity with a constant downward acceleration of 9.8 m/s^2. Note that throwing upward shows velocity decreasing to zero at the top, then increasing on the descent.

Solve a kinematic free-fall problem by selecting a reference, applying motion equations to find time and final speed, and compare upward versus downward throws.

Define vectors by magnitude and direction, using unit vectors i, j, k and Cartesian components, or polar form. Show how to compute magnitude and angle, and convert between representations.

Convert between polar and Cartesian vector representations by computing x and y components from magnitude and angle using cosine and sine, and apply Pythagoras to find magnitude and direction.

Learn to add and subtract vectors by partitioning into x, y, and z components, and by placing them head to tail to determine the resultant sum or difference.

Learn vector addition with two examples: convert velocities to x and y components, compute the change in velocity, and express the result in polar form as magnitude and direction.

Explore two-dimensional motion by treating x and y separately, with x acceleration zero and y acceleration -9.8 m/s², showing objects share the same vertical acceleration in free fall.

Explore two-dimensional motion with projectile and slope examples, deriving horizontal and vertical components, solving distances and times under gravity, using position functions to obtain instantaneous and average velocity and acceleration.