NEET · Physics

NEET Motion in Plane: Vectors, Projectiles and Circular Motion

Own the two-dimensional/vector-focused subset of official Unit 2: vector operations, resolution, relative velocity, projectile motion and uniform circular motion.

Subject: Physics
Official syllabus unit: Unit 2: Kinematics

In short

Motion in Plane applies vector reasoning to two-dimensional motion. Resolve vectors along chosen axes, treat horizontal and vertical projectile motion with their correct accelerations, and use radial acceleration for uniform circular motion. Projectile shortcut formulas require ideal conditions and must not be used blindly.

Subject faculty

Ashwini M.

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Physics • NEET

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Also in Physics: Kumar Gandharva Saxena

Syllabus mapping

Syllabus mapping
Unit	Topics
Focused part of a larger current official unit	Vector model first, Projectile motion, Relative velocity, Uniform circular motion

Unit
Focused part of a larger current official unit
Topics
Vector model first, Projectile motion, Relative velocity, Uniform circular motion

Before this chapter

Concepts in this chapter

1. Vector model first

Choose perpendicular axes and resolve each vector into components. Addition and subtraction are performed component-wise; a vector's magnitude is not generally the sum of component magnitudes. Scalar and vector products must be distinguished by their output and geometric meaning.

2. Projectile motion

In the ideal school-level projectile model, horizontal acceleration is zero and vertical acceleration is -g, with air resistance neglected and g treated as uniform. The horizontal and vertical motions share the same time variable. Range and maximum-height shortcuts depend on additional conditions, especially launch and landing at the same level for the standard range formula.

3. Relative velocity

Relative velocity is the vector difference v_A/B = v_A - v_B. Draw or resolve vectors instead of subtracting speeds as scalars unless the motion is strictly collinear.

4. Uniform circular motion

Uniform speed does not mean zero acceleration. The velocity direction changes continuously, producing inward radial acceleration of magnitude v^2/r = ω^2 r. The acceleration vector points toward the center.

5. Decision aids for this chapter

Vector-resolution diagram template

Projectile condition card showing when shortcut formulas are valid

Circular-motion velocity/acceleration direction diagram

Formula sheet

Vector components: A_x=A cosθ, A_y=A sinθ;. A
Vector components
Use when — A
Relative velocity: v_A/B = v_A - v_B. Vector equation; m s^-1. Use vector subtraction, not speed subtraction unless collinear.
Relative velocity
Use when — Vector equation; m s^-1. Use vector subtraction, not speed subtraction unless collinear.
Projectile position: x=(u cosθ)t; y=(u sinθ)t-(1/2)gt^2. Ideal projectile, constant downward g, no air resistance, axes with launch point as origin.
Projectile position
Use when — Ideal projectile, constant downward g, no air resistance, axes with launch point as origin.
Time of flight, same level: T = 2u sinθ/g. Requires launch and landing at same vertical level under the ideal projectile model.
Time of flight, same level
Use when — Requires launch and landing at same vertical level under the ideal projectile model.
Range, same level: R = u^2 sin(2θ)/g. Same-level launch/landing, constant g, no air resistance.
Range, same level
Use when — Same-level launch/landing, constant g, no air resistance.
Maximum height: H = u^2 sin^2θ/(2g). Vertical component reaches zero; same ideal assumptions.
Maximum height
Use when — Vertical component reaches zero; same ideal assumptions.
Uniform circular acceleration: a_c = v^2/r = ω^2 r. Magnitude of inward radial acceleration for uniform circular motion; m s^-2.
Uniform circular acceleration
Use when — Magnitude of inward radial acceleration for uniform circular motion; m s^-2.

Worked examples

A projectile is launched at 20 m s^-1 at 30° above horizontal and lands at the same level. Take g=10 m s^-2. Find time of flight and range.

Concept being tested: Projectile motion

Prompt: A projectile is launched at 20 m s^-1 at 30° above horizontal and lands at the same level. Take g=10 m s^-2. Find time of flight and range.

Decisive condition: Same-level launch/landing and ideal projectile conditions allow the shortcut formulas.

Method choice: Use T=2u sinθ/g and R=u^2 sin2θ/g.

Reasoning/calculation: T=2×20×0.5/10=2 s. R=400×sin60°/10≈34.6 m.

Unit/sign/condition check: Time in seconds, range in metres. Horizontal direction is positive; g magnitude is used in the shortcut formulas.

PI if answered incorrectly: Decision / Selection Error if same-level formulas are used without verifying the height condition.

Common mistakes and what they actually indicate

Subtracting relative speeds instead of velocity vectors
Knowledge gap
Why it happens
Preparation Intelligence classification: Knowledge Gap.
How it is corrected
Resolve directions and subtract vectors.
Using the standard range formula when launch and landing heights differ
Decision / selection error
Why it happens
Preparation Intelligence classification: Decision / Selection Error.
How it is corrected
Use component equations with the actual vertical condition.
Saying acceleration is zero in uniform circular motion because speed is constant
Knowledge gap
Why it happens
Preparation Intelligence classification: Knowledge Gap.
How it is corrected
Velocity changes direction; radial acceleration is nonzero.
Dropping component signs after choosing axes
Execution error
Why it happens
Preparation Intelligence classification: Execution Error.
How it is corrected
Carry signed components through the calculation.

FAQ