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Playbook

Kinematics and Motion

24 q · 25% HARD. Small chapter, heavy HARD load. v=u+at, s=ut+½at², v²=u²+2as plug-in dominates, plus V-T/X-T graph reading and the lone Vectors-and-Position subtopic at 67% HARD.

questions in the bank
24
tagged HARD
25%
subtopic(s)
4
worked examples
2

When you’ll see it

A v=u+at / s=ut+½at² plug-in, a V-T / X-T graph identification, a projectile range, a circular-motion average-acceleration over half-circle, or a vector position-time analysis.

How this chapter is tested

24 q in 10 years · 25% HARD — small chapter, heavy HARD load. Equations of Motion subtopic (15 q) dominates. The three equations v = u + at, s = ut + ½at², v² = u² + 2as hold ONLY for constant acceleration; piecewise motion requires applying them in segments.

V-T (velocity-time) graphs: slope = acceleration; area under curve = displacement. X-T (position-time) graphs: slope = velocity; curvature direction reveals acceleration sign. Most graph questions test mapping between an equation (v = u + at) and the correct graph shape (straight line with positive slope = u-intercept).

Vectors and Position (3 q, 67% HARD) is the toughest subtopic. Position vector r⃗ = x î + y ĵ + z k̂ as a function of t. Velocity = dr⃗/dt (component-wise), acceleration = dv⃗/dt. Magnitude of velocity = √(vₓ² + v_y² + v_z²). NDA's HARD shape: 'given r⃗(t), what's the angle of velocity with x-axis at t=1?'

The sub-skills

The rules and habits that decide whether you get a question right.

  • Three equations of motion (constant a)

    v = u + at (no s). s = ut + ½at² (no v). v² = u² + 2as (no t). Pick the equation that omits the unknown you don't need.

  • V-T / X-T graph reading

    Slope of V-T = acceleration. Area under V-T = displacement. Slope of X-T = velocity. V-T for v = u + at: line with slope a, y-intercept u.

  • Piecewise motion handling

    Two-phase problem (a₁ for t₁ seconds, then a₂ for t₂ seconds): compute v at end of phase 1 = u + a₁t₁; use it as initial for phase 2. Total distance = s_1 + s_2.

  • Circular motion — average acceleration over half circle

    Speed constant but velocity direction reverses. Δv⃗ = v_final − v_initial = −2v̂ × v. |Δv⃗| = 2v. Time for half circle = πR/v. |a_avg| = 2v / (πR/v) = 2v²/(πR).

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Kinematics and MotionHARD
The position vector of a particle is given by r⃗=3t2i^+2tj^+5k^\vec{r} = \sqrt{3}t^2\hat{i} + \sqrt{2}t\hat{j} + \sqrt{5}\hat{k}. Which one of the following statements is correct?

[Q57 · Apr · 2026]

Example 2Kinematics and MotionHARD
A vehicle starts from rest. In first t seconds it moves with acceleration 2 m/s2 and then in next 10 seconds with acceleration 5 m/s2. Total distance = 550 m. The value of time t is

[Q91 · Sep · 2024]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Applying constant-a equations to changing-a motion

    If a changes mid-motion, you CAN'T apply v² = u² + 2as across the whole motion. Must split into segments. Distractor option uses the equations naively.

  • Average acceleration vs average velocity

    Average velocity = (u+v)/2 for constant a (different formula for variable a). Average acceleration = Δv/Δt — uses CHANGE in v, not average of v.

Drill every kinematics and motion question

24 questions from the bank, scoped to 4 bundled subtopics.

Drill the 24 questions

Related playbooks

Often paired with this one — drill these next if you found the worked examples above tractable.