When a body experiences negative acceleration (retardation), the acceleration vector acts in a direction opposite to which of the following vectors?

Introduction / Context:
In kinematics, acceleration describes how the velocity of an object changes with time. When acceleration acts in the same direction as velocity, the object speeds up. When it acts in the opposite direction, the object slows down, and this is often called negative acceleration or retardation. This question asks you to identify which vector negative acceleration opposes.

Given Data / Assumptions:

• We describe motion using vectors: displacement, velocity, acceleration, force, and momentum.
• Negative acceleration means that the acceleration is directed opposite to the chosen positive direction of velocity.
• We assume straight line motion for simplicity.
• The options include force, displacement, velocity, and momentum.

Concept / Approach:
Velocity is the rate of change of displacement with time and points in the direction of motion. Acceleration is the rate of change of velocity with time. If acceleration has a component opposite to the velocity vector, it reduces the magnitude of the velocity, slowing the body down. This is the situation referred to as negative acceleration or retardation in elementary physics. While force is related to acceleration through Newton second law, the phrase negative acceleration is best understood as acceleration opposite to velocity, not necessarily opposite to displacement or momentum in every context.

Step-by-Step Solution:
Step 1: Consider an object moving to the right. We take motion to the right as the positive direction, so its velocity vector points to the right. Step 2: If the object is slowing down, its speed is decreasing even though it is still moving to the right for some time. Step 3: For speed to decrease, the acceleration must have a component opposite to the direction of velocity, which in this case is to the left. Step 4: This acceleration directed opposite to velocity is called negative acceleration or retardation when we have chosen the direction of velocity as positive. Step 5: Therefore, negative acceleration is in the direction opposite to the velocity vector.

Verification / Alternative check:
Mathematically, if velocity v is positive and decreasing, then dv/dt is negative, indicating acceleration a is negative with respect to the chosen coordinate axis. Graphs of velocity versus time for a braking car show a straight line sloping downwards, representing negative acceleration while velocity is still positive. This graphical interpretation again highlights that acceleration points opposite to velocity during slowing down motion, matching the conceptual description of negative acceleration.

Why Other Options Are Wrong:
Net force: Although net force and acceleration are in the same direction by Newton second law, the question asks what negative acceleration is opposite to, which is best expressed in terms of velocity, not force. Displacement: Displacement points from the initial to the final position and may not coincide with the instantaneous velocity or acceleration directions at all times. Momentum: Momentum is mass times velocity, so its direction is the same as velocity, but the standard explanation of negative acceleration is given directly in relation to velocity, not momentum.

Common Pitfalls:
Students may confuse negative acceleration with simply changing direction of motion. A body may have positive acceleration and yet change direction, as in circular motion, if the coordinate system is chosen differently. The key is to think of negative acceleration as acceleration that reduces the magnitude of velocity along its current direction of motion, which means it acts opposite to the velocity vector in that frame of reference.

Final Answer:
Negative acceleration, or retardation, acts in a direction opposite to the velocity of the body.