Verified Solution • 2025–26 Session moderate

QPage 48-49: Q11: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q11 Solution: In figure shows the x coordinate of a particle as a function of …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly infer the sign of acceleration from the sign of velocity or the direction of motion. Remember that acceleration is the second derivative of position ($a_x = d^2x/dt^2$), so its sign is determined solely by the graph's concavity: concave up implies $a_x > 0$ and concave down implies $a_x < 0$, regardless of whether the particle is moving left or right.

In figure shows the x coordinate of a particle as a function of time. Find the signs of vx and ax at t = t1, t = t2 and t = t3.

Multiple Choice Options

  • A
  • B
  • C
  • D

Step-by-Step Verified Solution

Detailed Explanation

  1. At t=t1t = t_1:
  2. Velocity (vxv_{x}) is positive (++): The position xx is increasing with time, meaning the slope of the graph at this point is positive.
  3. Acceleration (axa_{x}) is positive (++): The graph is curving upward (concave up), which indicates that the slope is increasing as time passes.
  4. At t=t2t = t_2:
  5. Velocity (vxv_{x}) is zero (00): The particle reaches its maximum position peak at this instant. The tangent line is perfectly horizontal, so the slope is zero.
  6. Acceleration (axa_{x}) is negative (−-): The curve is at a crest and bending downward (concave down), showing that the slope is changing from positive to negative (decreasing).
  7. At t=t3t = t_3:
  8. Velocity (vxv_{x}) is negative (−-): The position xx is decreasing with time, which means the tangent line slopes downward (negative slope).
  9. Acceleration (axa_{x}) is negative (−-): The graph continues to bend downward (concave down), meaning the velocity is becoming more negative (its value is decreasing).

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

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Chapter-3 Rest and Motion Kinematics
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 1
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring