📘 Motion: Physics Foundations

What you’ll learn

1. Position, Displacement, and DistanceDefine position, displacement, and distance with vector and scalar distinctions in one dimension.Position is a coordinate on a reference frame. Displacement is the net vector change between initial and final positions. Distance is the scalar path length traveled. These distinctions become essential when later calculating velocity and acceleration from real trajectories.
2. Speed and VelocityDifferentiate average versus instantaneous speed and velocity using limits and derivatives.Speed is the magnitude of velocity. Average velocity equals displacement over time interval. Instantaneous velocity is the derivative of position. The sign of velocity indicates direction along a chosen axis and sets up later acceleration calculations.
3. Acceleration in One DimensionCalculate average and instantaneous acceleration and relate it to changes in velocity.Acceleration is the rate of change of velocity. Constant acceleration allows use of simple kinematic relations. The direction of acceleration determines whether speed increases or decreases. These definitions prepare students for the kinematic equations that follow.
4. Kinematic Equations for Constant AccelerationApply the four standard kinematic equations to solve problems with constant acceleration.The equations link initial velocity, final velocity, acceleration, time, and displacement. Each equation is derived from the definitions of velocity and acceleration under constant acceleration. Choosing the right equation eliminates unnecessary variables. Worked examples demonstrate substitution and unit consistency.
5. Motion Graphs and Their SlopesInterpret position-time, velocity-time, and acceleration-time graphs and extract physical quantities from slopes and areas.Slope of position-time graph equals velocity. Slope of velocity-time graph equals acceleration. Area under velocity-time graph equals displacement. These graphical relationships allow qualitative and quantitative analysis of real motion data.
6. Vectors in Two DimensionsResolve vectors into components and perform addition using both graphical and analytical methods.Any vector is decomposed using sine and cosine of its direction angle. Component addition follows the parallelogram rule or separate x-y summation. Resultant magnitude and direction are recovered with Pythagoras and tangent. Component methods simplify two-dimensional motion problems.
7. Projectile MotionSeparate horizontal and vertical motion to solve projectile problems under constant gravity.Horizontal acceleration is zero; vertical acceleration is g. Time of flight is found from vertical displacement returning to zero. Range depends on launch speed, angle, and g. The parabolic trajectory emerges from these independent motions.
8. Newton's Laws of MotionState and apply Newton's three laws to distinguish equilibrium from accelerated motion.First law defines inertial frames and net-force zero. Second law quantifies acceleration as net force over mass. Third law identifies action-reaction pairs. These laws unify the description of all classical motion.
9. Applying Newton's Second LawDraw free-body diagrams and write Newton's second-law equations for systems with multiple forces.Net force equals mass times acceleration in each dimension. Tension, normal force, and weight components are identified from diagrams. Simultaneous equations solve for unknowns. Consistent sign conventions prevent common errors.
10. Friction and Drag ForcesIncorporate static friction, kinetic friction, and viscous drag into Newton's laws.Static friction prevents relative motion up to μ_s N. Kinetic friction opposes sliding at μ_k N. Drag increases with speed and eventually balances driving force at terminal velocity. These non-conservative forces dissipate mechanical energy.
11. Work, Energy, and the Work-Energy TheoremCalculate work by constant and variable forces and relate it to kinetic-energy change.Work is force dot displacement. Net work equals change in kinetic energy. Potential energy is introduced for conservative forces. The theorem provides an alternative to Newton's laws for speed calculations.
12. Momentum, Impulse, and CollisionsApply conservation of momentum and distinguish elastic from inelastic collisions.Momentum is conserved when net external force is zero. Impulse equals change in momentum. Elastic collisions conserve kinetic energy; inelastic collisions do not. Center-of-mass frame simplifies analysis of two-body interactions.

Questions this course answers

Grounded in trusted sources

• OpenStax
• NASA
• National Institute of Standards and Technology
• OpenStax University Physics, Motion and Newton's Laws, https://openstax.org/books/university-physics-volume-1/pages/2-introduction
• PhET Interactive Simulations, Forces and Motion, https://phet.colorado.edu/
• Khan Academy, One-dimensional motion, https://www.khanacademy.org/science/physics
• MIT OCW, Classical Mechanics lecture notes, https://ocw.mit.edu/

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