Verified Solution • 2025–26 Session moderate

QP 50-51: Q3: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics P 50-51: Q3 Solution: Pick the correct statements:

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume that zero average velocity implies zero instantaneous velocity at some point in any motion, but this is only guaranteed in one-dimensional motion due to the continuity of the position function. In multi-dimensional motion, a particle can have zero net displacement (e.g., circular path) while maintaining a non-zero instantaneous velocity throughout.

Pick the correct statements:

Multiple Choice Options

  • A (a) Average speed of a particle in a given time is never less than the magnitude of the average velocity.
  • B (b) It is possible to have a situation in which ∣dv⃗/dt∣≠0|d\vec{v}/dt| \neq 0 but d∣v⃗∣/dt=0d|\vec{v}|/dt = 0.
  • C (c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.
  • D (d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed).

Step-by-Step Verified Solution

Statements 1, 2, and 3 are correct, while Statement 4 is incorrect.


  1. Statement 1: Correct
  2. Average speed is defined as total distanceΔt\frac{\text{total distance}}{\Delta t}, whereas the magnitude of average velocity is ∣displacement∣Δt\frac{\vert{}\text{displacement}\vert{}}{\Delta t}. Since total path distance is always greater than or equal to the magnitude of displacement (distance≥∣displacement∣\text{distance} \ge \vert{}\text{displacement}\vert{}), average speed is never less than the magnitude of average velocity.
  3. Statement 2: Correct
  4. ∣dvdt∣\left\vert{}\frac{d\mathbf{v}}{dt}\right\vert{} represents the magnitude of the acceleration vector (∣a∣\vert{}\mathbf{a}\vert{}), while d∣v∣dt\frac{d\vert{}\mathbf{v}\vert{}}{dt} represents the rate of change of speed (tangential acceleration). In Uniform Circular Motion, speed remains constant (d∣v∣dt=0\frac{d\vert{}\mathbf{v}\vert{}}{dt} = 0), but the direction of velocity constantly changes, resulting in a non-zero centripetal acceleration (∣dvdt∣≠0\left\vert{}\frac{d\mathbf{v}}{dt}\right\vert{} \neq 0).
  5. Statement 3: Correct
  6. In multi-dimensional motion (such as a particle moving in a closed circular path at a constant non-zero speed), the particle returns to its starting point, making total displacement and average velocity equal to zero. However, its instantaneous speed is never zero at any point during the trip.
  7. Statement 4: Incorrect
  8. In one-dimensional (straight-line) motion, an average velocity of zero means the net displacement is zero (x(t1)=x(t2)x(t_1) = x(t_2)). Since infinite acceleration is prohibited, the position function x(t)x(t) is continuous and differentiable. By Rolle's Theorem, there must be at least one instant in the interval where the derivative dxdt=v(t)=0\frac{dx}{dt} = v(t) = 0. The particle must temporarily stop to reverse direction.

All Questions in this Chapter

QP 49-50: Q1 QP 49-50: Q2 QP 49-50: Q3 QP 49-50: Q4 QP 49-50: Q5 QP 49-50: Q6 QP 49-50: Q7 QP 49-50: Q8 QP 49-50: Q9 QP 49-50: Q10 QP 49-50: Q11 QP 49-50: Q12 QP 49-50: Q13 QP 50-51: Q1 QP 50-51: Q2 QP 50-51: Q3 QP 50-51: Q4 QP 50-51: Q5 QP 50-51: Q6 QP 50-51: Q7 QP 50-51: Q8 QP 50-51: Q9 QP 50-51: Q10 QP 51-54: Q1 QP 51-54: Q2 QP 51-54: Q3.1 QP 51-54: Q3.2 QP 51-54: Q3.3 QP 51-54: Q3.4 QP 51-54: Q4.1 QP 51-54: Q4.2 QP 51-54: Q5 QP 51-54: Q6 QP 51-54: Q7 QP 51-54: Q8.1 QP 51-54: Q8.2 QP 51-54: Q8.3 QP 51-54: Q9.1 QP 51-54: Q9.2 QP 51-54: Q10 QP 51-54: Q11 QP 51-54: Q12 QP 51-54: Q13 QP 51-54: Q14 QP 51-54: Q15.1 QP 51-54: Q15.2 QP 51-54: Q15.3 QP 51-54: Q16 QP 51-54: Q17 QP 51-54: Q18.1 QP 51-54: Q18.2 QP 51-54: Q19 QP 51-54: Q20 QP 51-54: Q21 QP 51-54: Q22 QP 51-54: Q23.1 QP 51-54: Q23.2 QP 51-54: Q23.3 QP 51-54: Q24 QP 51-54: Q25.1 QP 51-54: Q25.2 QP 51-54: Q25.3 QP 51-54: Q26 QP 51-54: Q27 QP 51-54: Q28 QP 51-54: Q29 QP 51-54: Q30 QP 51-54: Q31 QP 51-54: Q32.1 QP 51-54: Q32.2 QP 51-54: Q32.3 QP 51-54: Q33.1 QP 51-54: Q33.2 QP 51-54: Q34 QP 51-54: Q35 QP 51-54: Q36 QP 51-54: Q37 QP 51-54: Q38 QP 51-54: Q39 QP 51-54: Q40 QP 51-54: Q41 QP 51-54: Q42 QP 51-54: Q43.1 QP 51-54: Q43.2 QP 51-54: Q44 QP 51-54: Q45 QP 51-54: Q46.1 QP 51-54: Q46.2 QP 51-54: Q47.1 QP 51-54: Q47.2 QP 51-54: Q48 QP 51-54: Q49.1 QP 51-54: Q49.2 QP 51-54: Q50 QP 51-54: Q51 QP 51-54: Q52 QPage 48-49: Q1 QPage 48-49: Q2 QPage 48-49: Q3 QPage 48-49: Q4 QPage 48-49: Q5 QPage 48-49: Q6 QPage 48-49: Q7 QPage 48-49: Q8 QPage 48-49: Q9 QPage 48-49: Q10.1 QPage 48-49: Q10.2 QPage 48-49: Q10.3 QPage 48-49: Q11 QPage 48-49: Q12 QPage 48-49: Q13 QPage 48-49: Q14

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