Question

Which one of the following statements is correct for a moving body?

• A. If its velocity changes, its speed must change and it must have some acceleration
• B. If its speed changes, its velocity must change and it must have some acceleration
• C. If its speed changes but direction of motion does not change, its velocity will remain constant
• D. None of the above

Hint:

Speed is the magnitude of velocity. Any change in speed is a change in velocity.

Answer 1

The Correct Option is B

Step 1: Concept
Velocity is a vector quantity (speed + direction). Acceleration is the rate of change of velocity.
Step 2: Analysis of Options
- (A) is false because velocity can change due to direction alone (e.g., uniform circular motion) while speed stays constant. - (C) is false because a change in speed directly changes the magnitude of the velocity vector.
Step 3: Reasoning for Option B
If speed changes, the magnitude of the velocity vector changes. Since velocity changes, there must be acceleration.
Step 4: Conclusion
Hence, option (B) is logically correct.
Final Answer:(B)