Kinematics: Motion in a Straight Line & Plane
একমাত্রিক ও দ্বিমাত্রিক গতি
Mathematical modeling of particle motion using calculus: position vectors, velocity, acceleration, projectile motion, and relative velocity.
Target Learning Objectives
- Differentiate between scalar distance/speed and vector displacement/velocity.
- Derive kinematic equations of uniformly accelerated motion using calculus and graphical methods.
- Analyze projectile motion trajectories, maximum height, time of flight, and horizontal range.
- Formulate relative velocity problems in one and two dimensions.
Governing Physical Concepts
- Instantaneous Velocity & Acceleration (dx/dt, dv/dt)
- Equations of Motion: v = u + at, s = ut + 1/2at^2, v^2 = u^2 + 2as
- Calculus Analysis of Non-Uniform Acceleration
- Parabolic Trajectory of 2D Projectiles
- Relative Velocity in River-Boat and Rain-Man Configurations
Chapter Topics & Breakdown
Position, Displacement & Velocity Calculus
Calculus foundations of instantaneous rates of change in 1D kinematics.
Kinematic Equations & Graphical Analysis
Derivation of uniform acceleration equations and interpreting slope and area of s-t, v-t, and a-t graphs.
2D Projectile Motion on Horizontal & Inclined Planes
Orthogonal decomposition of velocity, parabolic trajectories, time of flight, and maximum range.
Relative Velocity in 1D & 2D Vectors
Reference frame vector differences, river-swimmer crossings, and rain-umbrella orientation.
Study Materials for this Chapter
Kinematics: First-Principles Lecture Notes & Derivations
Detailed, rigorous academic notes covering calculus differentiation and integration for position, velocity, and acceleration vectors, with step-by-step proofs.
Quick Revision Summary
“Separate orthogonal x and y components completely in two-dimensional motion. The only shared scalar is time (t).”
- •Horizontal velocity remains constant in ideal projectile motion: ux = u cos θ.
- •Vertical acceleration is -g under free fall.
- •Area under v-t graph yields displacement.
Structured Practice Roadmap
Progressive numericals covering calculus kinematics, projectile launch angles, and relative velocity vectors.
Unit Diagnostic 02: Kinematics
Assessment Architecture • Academic Evaluation SpecificationTimed sectional examination testing 1D calculus and 2D projectile mechanics.