To determine the correct statement regarding a particle moving in a straight line, let's analyze each option carefully. Understanding the relationships between velocity, acceleration, and position is crucial in physics, particularly in kinematics. Here’s a breakdown of each statement:
Analyzing the Statements
Option A: If the velocity and acceleration have opposite signs, the particle is slowing down.
This statement is actually incorrect. When velocity and acceleration have opposite signs, the particle is indeed slowing down. For example, if a particle is moving to the right (positive velocity) and has a negative acceleration (deceleration), it will slow down. Therefore, this statement is true.
Option B: If the position vector and velocity vector have opposite signs, the particle is moving towards the origin.
This statement can be misleading. The position vector indicates the particle's location relative to the origin, while the velocity vector indicates the direction of motion. If they have opposite signs, it means the particle is moving away from the origin, not towards it. Thus, this statement is false.
Option C: If the velocity is zero at an instant, the acceleration should be zero at that point.
This statement is also incorrect. A particle can have zero velocity while still experiencing acceleration. For instance, consider a ball thrown upwards; at its highest point, the velocity is zero, but the acceleration due to gravity is still acting on it. Therefore, this statement is false.
Option D: If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.
This statement is not necessarily true. A particle can have a velocity of zero at certain points during a time interval while still experiencing acceleration. For example, if a car comes to a stop (velocity is zero) but is still in the process of decelerating, the acceleration is not zero. Thus, this statement is false.
Conclusion
After evaluating all the options, the correct statement is:
- A) If the velocity and acceleration have opposite signs, the particle is slowing down.
This understanding is fundamental in kinematics, as it helps us analyze motion effectively. Remember, the relationships between these vectors are key to predicting how a particle will behave in different scenarios.
