Paper II · Part B — Physics

Motion: Velocity and Acceleration

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Core5 mapped NDA questions

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Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.

Concept

Kinematics describes motion using displacement, velocity and acceleration. Velocity is the rate of change of displacement; acceleration is the rate of change of velocity.

The three equations of motion link these for uniform acceleration.

Key Points & Formulas

Speed is scalar; velocity is a vector (has direction).
Equations of motion: v = u + at; s = ut + ½at²; v² = u² + 2as.
Uniform velocity ⇒ zero acceleration.
Acceleration unit: m/s².

Worked Example

Q. A car starting from rest accelerates at 2 m/s² for 5 s. Find its final velocity.

u = 0, a = 2 m/s², t = 5 s.

v = u + at = 0 + 2×5 = 10 m/s.

Common traps

Reading the prompt too quickly and missing a qualifier.
Memorising the result without checking when it applies.
Skipping units, signs, chronology or the final reasonableness check.

NDA shortcuts

State the governing rule before substituting values.
Eliminate impossible options before doing full calculation.

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5 NDA questions

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Question 1

NDA I 2026

The position vector of a particle is given by $\begin{array}{l}\vec{r} = \sqrt{3}\,t^2\,\hat{i} + \sqrt{2}\,t\,\hat{j} \\ + \sqrt{5}\,\hat{k}\end{array}$ . Which one of the following statements is correct?

Question 2

NDA I 2025

A car has an initial velocity of 12 m/s and is brought to rest over a distance of 45 m. The acceleration of the car is

Question 3

NDA II 2024

Starting from rest a vehicle accelerates at the rate of 2 m/s² towards east for 10 s. It then stops suddenly. It then accelerates again at a rate of 4√2 m/s² for next 10 s towards south and then again comes to rest. The net displacement of the vehicle from the starting point is

Question 4

NDA II 2024

A vehicle starts moving along a straight line path from rest. In first t seconds it moves with an acceleration of 2 m/s² and then in next 10 seconds it moves with an acceleration of 5 m/s². The total distance travelled by the vehicle is 550 m. The value of time t is

Question 5

NDA II 2024

Which one among the following diagrams may correctly represent the motion of a skydiver during a jump ?

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