Verified Solution • 2025–26 Session moderate

QP 49-50: Q1: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics P 49-50: Q1 Solution: A motor car is going due north at a speed of . It makes a 90°…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often mistakenly calculate the change in velocity as the vector sum ($\mathbf{v}_i + \mathbf{v}_f$) or simply the difference in magnitude, leading to incorrect directions like North-West. Always compute $\Delta \mathbf{v} = \mathbf{v}_f - \mathbf{v}_i$ to ensure the resulting vector points from the tip of the initial velocity to the tip of the final velocity.

A motor car is going due north at a speed of 50 km/h50 \text{ km/h}. It makes a 90° left turn without changing speed. The change in the velocity of the car is about:

Multiple Choice Options

  • A 50 km/h50 \text{ km/h} towards west
  • B 70 km/h70 \text{ km/h} towards south-west
  • C 70 km/h70 \text{ km/h} towards north-west
  • D zero

Step-by-Step Verified Solution

Only statement **(b)** is correct. * **(a) Incorrect** The car initially moves due north with velocity
v⃗i=50j^ km/h.\vec v_i=50\hat j\ \text{km/h}.
After making a 90∘90^\circ left turn, it moves due west with the same speed:
v⃗f=−50i^ km/h.\vec v_f=-50\hat i\ \text{km/h}.
Therefore,
Δv⃗=v⃗f−v⃗i=−50i^−50j^.\Delta\vec v=\vec v_f-\vec v_i =-50\hat i-50\hat j.
The magnitude is
∣Δv⃗∣=502+502=502≈70 km/h.|\Delta\vec v|=\sqrt{50^2+50^2}=50\sqrt2\approx70\ \text{km/h}.
Hence the change is not simply 50 km/h50\ \text{km/h} towards west. * **(b) Correct** The change in velocity has equal westward and southward components, each equal to 50 km/h50\ \text{km/h}. Thus its magnitude is 502≈70 km/h50\sqrt2\approx70\ \text{km/h} and its direction is south-west. * **(c) Incorrect** The change in velocity has both westward and southward components. Therefore, it points south-west, not north-west. * **(d) Incorrect** Although the speed remains unchanged, the direction of velocity changes by 90∘90^\circ. Hence the velocity changes.

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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