QPage 48-49: Q8: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q8 Solution: If a particle is accelerating, it is either speeding up or…
If a particle is accelerating, it is either speeding up or speeding down. Do you agree ...
Step-by-Step Verified Solution
This is a classic trick question that exposes a very common misconception. The short answer is:
No, I do not fully agree. The statement is only partially correct because it confuses acceleration (a vector) with speeding up/slowing down (changes in speed only).
Step 1: What does "accelerating" actually mean?
In physics, acceleration is defined as the rate of change of velocity.
Since velocity is a vector (it has both magnitude and direction), acceleration can change velocity in two distinct ways:
Type of Change | Effect on Motion |
Change in magnitude (speed) | Speeding up or slowing down |
Change in direction | Turning/changing path without changing speed |
Step 2: Breaking down the statement
"If a particle is accelerating, it is either speeding up or speeding down."
This statement assumes that acceleration only affects speed. That is false.
Here are the three possible scenarios when a particle accelerates:
Case 1: Acceleration parallel to velocity → Speed changes
- Same direction as velocity → Particle speeds up (speed increases).
- Opposite direction to velocity → Particle slows down (speed decreases).
✅ The statement is correct for this case.
Case 2: Acceleration perpendicular to velocity → Direction changes, speed constant
- Example: Uniform circular motion.
- The acceleration (centripetal) is always perpendicular to the velocity.
- The speed remains constant, but the direction of motion keeps changing.
- The particle is accelerating (because velocity is changing), but it is neither speeding up nor slowing down.
❌ The statement is incorrect for this case.
Case 3: Acceleration has both parallel and perpendicular components
- Example: A car turning a corner while simultaneously pressing the accelerator or brake.
- Speed changes (due to parallel component) and direction changes (due to perpendicular component).
- The particle is accelerating, and it is either speeding up or slowing down as well as turning.
✅ The statement is correct for this case, but incomplete because it ignores the change in direction.
Step 3: Corrected Statement
A physically accurate version would be:
"If a particle is accelerating, its velocity is changing. This could mean it is speeding up, slowing down, changing direction, or any combination of these."
Step 4: Summary Table
Situation | Acceleration? | Speeding up or down? | Statement holds? |
Car speeding up in a straight line | ✅ Yes | ✅ Speeding up | ✅ Yes |
Car braking in a straight line | ✅ Yes | ✅ Slowing down | ✅ Yes |
Car turning at constant speed (circular motion) | ✅ Yes | ❌ Neither | ❌ No |
Car turning while accelerating | ✅ Yes | ✅ Speeding up (plus turning) | ✅ Yes, but incomplete |
Car turning while braking | ✅ Yes | ✅ Slowing down (plus turning) | ✅ Yes, but incomplete |
Final Answer
No, I do not agree with the statement.
A particle can be accelerating without speeding up or slowing down—for example, in uniform circular motion, where the acceleration is perpendicular to the velocity and only changes the direction of motion, not the speed.
The correct statement is: Acceleration means velocity is changing, which can involve a change in speed, a change in direction, or both.