QPage 48-49: Q2: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q2 Solution: When a particle moves with constant velocity, its average…
Students often incorrectly equate velocity and speed by ignoring that velocity is a vector while speed is a scalar. Remember that a vector can only be equal to another vector, not a scalar; you may only equate the magnitude of velocity to speed.
When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal....
Multiple Choice Options
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Step-by-Step Verified Solution
This statement is only partially correct—and in fact, it contains a major conceptual error. Let's break it down carefully:
The Statement
"When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal."
1. Average velocity vs. Instantaneous velocity – Equal (Correct)
For a particle moving with constant velocity (meaning constant magnitude AND constant direction):
- Instantaneous velocity = the velocity at any given instant = v (a vector).
- Average velocity = total displacement ÷ total time.
Since displacement = v × t, and total time = t, then:
Average velocity = (v × t) / t = v
So yes, average velocity and instantaneous velocity are equal in this case.
✅ This part is correct.
2. Instantaneous velocity vs. Speed – Not equal (Incorrect)
Here is the critical mistake:
- Instantaneous velocity is a vector (it has both magnitude and direction).
- Speed is a scalar (it has only magnitude; no direction).
They are different types of physical quantities and can never be "equal" in the strict physical sense, just as you cannot say "5 meters north" equals "5 meters."
What you can say is:
The magnitude of instantaneous velocity equals the instantaneous speed.
But the velocity itself (with direction) is not equal to the speed (without direction).
❌ This part is false.
3. Average velocity vs. Speed – Not equal (Incorrect)
Similarly:
- Average velocity is a vector (displacement/time).
- Speed (whether average or instantaneous) is a scalar (distance/time).
Even if the particle moves in a straight line without reversing direction, the magnitudes may be numerically the same, but the quantities themselves are fundamentally different.
For example:
- A car moves at a constant velocity of 10 m/s due East.
- Its speed is 10 m/s.
You can say the magnitude of the average velocity equals the speed, but you cannot say the average velocity equals the speed.
❌ This part is also false.
Corrected Statement
A physically accurate version would be:
"When a particle moves with constant velocity, its average velocity equals its instantaneous velocity. The magnitude of both equals the instantaneous speed. However, velocity (a vector) and speed (a scalar) are never 'equal'—only their numerical magnitudes can be the same in this case."
Quick Summary Table
Comparison | Equal? | Reason |
Average velocity vs. Instantaneous velocity | ✅ Yes | Constant velocity means displacement/time = velocity at any instant. |
Instantaneous velocity vs. Speed | ❌ No | One is a vector, the other is a scalar. Different physical quantities. |
Average velocity vs. Speed | ❌ No | One is a vector, the other is a scalar. Different physical quantities. |
Magnitude of instantaneous velocity vs. Instantaneous speed | ✅ Yes | By definition, speed is the magnitude of velocity. |
Final Verdict
The statement is partly true but fundamentally incorrect because it confuses vectors with scalars. If the particle moves in a straight line without changing direction, the numerical values of average velocity, instantaneous velocity, and speed may all be the same number (e.g., 10 m/s)—but physically and mathematically, velocity and speed are not "equal" to each other because they are different types of quantities. Only the magnitudes are equal.