Verified Solution • 2025–26 Session moderate

QP 50-51: Q6: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics P 50-51: Q6 Solution: The velocity of a particle is zero at .

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently assume that if a particle’s velocity is zero at an instant (e.g., $t=0$), its acceleration must also be zero. In reality $a=\frac{dv}{dt}$ can be non‑zero at that moment (e.g., a body dropped from rest has $v(0)=0$ but $a(0)=g$); only a zero acceleration over an interval guarantees constant (zero) velocity.

The velocity of a particle is zero at t=0t = 0.

Multiple Choice Options

  • A (a) The acceleration at t=0t = 0 must be zero.
  • B (b) The acceleration at t=0t = 0 may be zero
  • C (c) If the acceleration is zero from t=0t = 0 to t=10t = 10 s, the speed is also zero in this interval.
  • D (d) If the speed is zero from t=0t = 0 to t=10t = 10 s the acceleration is also zero in this interval.

Step-by-Step Verified Solution

Statements (b), (c), and (d) are correct.


  1. (a) Incorrect
  2. The acceleration at t=0t = 0 does not have to be zero. For instance, a body dropped from rest has zero velocity at t=0t = 0, but its acceleration is g≠0g \neq 0.


  1. (b) Correct
  2. The acceleration at t=0t = 0 can be zero if the particle remains at rest or begins moving smoothly with a(0)=0a(0) = 0 (for example, motion defined by x(t)=t3x(t) = t^3, where both v(0)=0v(0) = 0 and a(0)=0a(0) = 0).


  1. (c) Correct
  2. If acceleration a=dvdt=0a = \frac{dv}{dt} = 0 throughout the interval t=0t = 0 to 10 s10\text{ s}, velocity remains constant. Since v(0)=0v(0) = 0, velocity stays 00 for the entire interval, making speed (∣v∣\vert{}v\vert{}) zero as well.


  1. (d) Correct
  2. If the speed is zero throughout t=0t = 0 to 10 s10\text{ s}, the velocity vector remains constantly zero. The time derivative of a constant zero velocity is zero, so acceleration is zero at every instant in that interval.


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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