QPage 48-49: Q3: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q3 Solution: A car travels at a speed of 60 km/hr due north and the other at …
Do not assume two velocities are equal or comparable solely because their numerical magnitudes (speeds) are identical; since velocity is a vector, both magnitude and direction must match for equality, and 'greater than' comparisons are only valid for collinear vectors.
A car travels at a speed of 60 km/hr due north and the other at a speed of 60 km/hr due east. Are the velocities equal? If no, which one....
Multiple Choice Options
- A
- B
- C
- D
Step-by-Step Verified Solution
Are the velocities equal?
No, they are not equal.
Velocity is a vector quantity, which means it has both magnitude and direction.
- Car A: velocity = 60 km/hr due North
- Car B: velocity = 60 km/hr due East
Even though the magnitudes (speed) are identical (60 km/hr), the directions are different (North vs. East).
For two vectors to be equal, both their magnitude and direction must be exactly the same. Since North ≠ East, the velocities are not equal.
Which one is greater?
Neither is "greater" than the other.
Here is why:
- Magnitude-wise: Both have the same speed (60 km/hr), so one does not have a larger numerical value than the other.
- Direction-wise: "Greater" has no meaning for direction. You cannot say North is "greater" than East—they are just different perpendicular directions.
In vector terms, you can only compare vectors if they are collinear (along the same line). For example, you can say 60 km/hr North is "greater" than 40 km/hr North. But when directions differ, comparison using "greater than" or "less than" is meaningless.
Is the question irrelevant?
No, the question is highly relevant.
It is a classic pedagogical question designed to expose a very common misconception: confusing speed (scalar) with velocity (vector). Many students instinctively want to say "they are the same" because the numbers match, but the question forces you to recognize that direction is an essential part of velocity.
If the question had asked:
"Are the speeds equal?"
Then the answer would be yes (both are 60 km/hr).
But because it asks about velocities, the direction matters, and the answer is a firm no.
Quick Summary Table
Quantity | Car A | Car B | Equal? |
Speed (scalar) | 60 km/hr | 60 km/hr | ✅ Yes |
Velocity (vector) | 60 km/hr North | 60 km/hr East | ❌ No |
Which is greater? | Neither | Neither | Comparison is meaningless because directions differ. |
Final Verdict
The velocities are not equal because their directions differ.
Neither velocity is greater than the other—you can only compare speeds (magnitudes), which are equal, or compare vectors along the same line.
The question is not irrelevant; it is a valuable tool for understanding the vector nature of velocity