Definition and use of units to show that free-fall time is proportional to √(h) and 1/√(g).

Measurements of falling times for different heights and comparison to dimensional analysis.

Definitions and distinctions between the two, using graph on board.

Definition of instantaneous velocity using tangent line to a graph, and of instantaneous speed using velocity from graph.

Average velocity example using bullet in demonstration.

Average acceleration equation with example and two short demos; acceleration as v' and x''; and finding sign of acceleration from a graph.

Calculating v(t) and a(t) from x(t); interpreting zeroes of x, v, and a; and graphing x vs. t.

Kinematics equations for x, v, and a for constant a; example using gravity.

Free-fall of object, using strobe-lighting of 2 frequencies to show increasing v.

Distinction between vectors and scalars; addition and subtraction of vectors.

Decomposition of 3D vector into components and use of angles θ and φ with example.

Dot product formulas using components and using cos(θ), with two brief examples.

Calculation of the cross product using the determinant of a component matrix, with the determinant explicitly expanded.

Cross product calculation using sin(θ); finding direction by corkscrew method; and importance of right-handed coordinates.

Definition of dot product, with example; properties of cross products.

Worked example of kinematics problem; determining x, v, and a at all times from graph of x vs. t.

Average velocity in 1D kinematics; constructing velocity graph from x vs. t.

Ideal particle simplification; definition of average velocity, with examples; definition of instantaneous velocity, with examples; uniform linear motion; speed of rifle bullet example.

Definition of average acceleration; definition of instantaneous acceleration, with examples; uniformly accelerated motion, with examples.

Definition, including equation of motion due to gravity, with examples.

Relative velocity and acceleration defined; special case of constant acceleration.

Definition of kinematics; coordinate system in one dimension; definitions of position, displacement, average velocity, instantaneous velocity, average acceleration, instantaneous acceleration.

Area under acceleration vs. time graph; area under velocity vs. time graph; velocity as the integral of acceleration; position as the integral of velocity, with example.

Showing consistency of dimensions, and finding new dimensions for scaled-up equation.

Solution (PDF)^#

5-part 1D kinematics; one person walks half time and runs the other; the other person walks half distance and runs the other.

Solution (PDF)^#

Sketching velocity curves within displacement and acceleration parameters.

Solution (PDF)^#

3-part problem; graphing and finding time to collision for balls dropped consecutively.

Solution (PDF)^#

Displacement, velocity, and acceleration of objects moving in one dimension. Solution not included.

One dimensional motion of two vehicles.

Solution (PDF)

Comparing the displacement of an object and its distance traveled. Solution not included.

Motion of a ball thrown vertically. Solution not included.

Determining velocity from a position vs. time graph. Solution not included.

Difference in speed between two falling stones. Solution not included.

Difference in position between two falling stones. Solution not included.

Time interval between two falling stones hitting the ground. Solution not included.

Velocities of two vertically thrown balls. Solution not included.

Relative motion of two falling stones.

Solution (PDF)^#

Modelling the motion of a person catching a streetcar.

Solution (PDF)^#

Measuring the acceleration of gravity by timing a falling ball.

Solution (PDF)

Motion of two runners in a race.

Solution (PDF)

Motion of a falling object in an elevator viewed from multiple reference frames.

Solution (PDF)

10-part 1D kinematics problem; finding and graphing x, v, a.

Solution (PDF)^#

Calculating travel time dependent and independent of wind.

Solution (PDF)

4-part problem; finding position, acceleration, and average speed from v vs. t. Solutions are given below the problems.

3-part problem; calculating time for round trip, average velocity, and average speed. Solutions are given below the problems.

Position, velocity, and acceleration of a runner.

Solution (PDF)

Finding acceleration as a function of time from equations for position.

Solution (PDF)

Motion of two cars, one at constant velocity and the other decelerating.

Solution (PDF)

Vertical motion of a rocket.

Solution (PDF)

Motion of and forces acting on a jumping basketball player.

Solution (PDF)

Average speed of a space shuttle during fuel consumption.

Solution (PDF)^#

Motion of two runners in a race.

Solution (PDF)^#

3-part 3D kinematics and 2-part 1D kinematics problem about a moving particle.

Solution (PDF)

6-part 1D kinematics of moving particle involving calculation and graphing of velocity and acceleration.

Solution (PDF)