Mastering Kinematics for JEE/NEET: Formulas, Graphs and Typical Traps

Introduction

Kinematics appears everywhere in competitive exams. Mastering graphs, signs and relative motion prevents easy mistakes and frees up time for tougher sections.

Background / Prerequisites

• Comfortable with differentiation/integration basics.
• Able to switch between vector and component forms.

Core Concepts

• Equations of motion for constant acceleration.
• Graph interpretations (x-t, v-t, a-t).
• Relative velocity and frames.
• Projectile motion decomposed into horizontal and vertical parts.

Detailed Explanation

Formulas to revisit

• \(v = u + a t\)
• \(s = ut + \tfrac{1}{2} a t^2\)
• \(v^2 = u^2 + 2 a s\)
• Projectile range \(R = (u^2 \sin 2\theta)/g\)

Graph tips

• Slope of x-t graph = velocity, slope of v-t = acceleration, area under v-t = displacement.
• Curved segments often mean changing acceleration; identify where slope is positive or negative.

Relative motion

• Velocity of A w.r.t B = v_A - v_B.
• Use this for rain-man problems or boats in streams.

Typical traps

• Mixing up signs when switching directions.
• Assuming acceleration is constant when it is not stated.
• Forgetting that average velocity = displacement/time, not average of speeds.

Examples / Applications

• Analyze two-particle pursuit problems with relative velocity diagrams.
• Sketch v-t graph for an elevator ride with start-stop phases.
• Break complex projectile paths into horizontal and vertical tables.

Common Mistakes & Tips

• Jumping straight to formulas without sketching. A quick diagram often exposes hidden information.
• Ignoring units. Keep conversions (km/h to m/s) at the top of your sheet.
• Attempting to memorize graph shapes instead of understanding slopes and areas.

Summary / Key Takeaways

• Consistent handling of signs and frames reduces silly mistakes.
• Graph literacy speeds up comprehension of word problems.
• Keep a curated sheet of 15–20 must-know kinematics problems.

Further Reading / Related Topics

• Relative motion in rotating frames.
• Motion under variable acceleration.
• Using calculus to derive kinematics results.