Q.Explain the physical meaning of a negative acceleration (retardation) with the help of the example of a car slowing down as it approaches a red traffic light.

[!TLDR] Negative (retarding) acceleration acts opposite to the direction of velocity, so speed decreases with time even while velocity keeps its original sign until the body stops. [!ANSWER] A braking car has a forward velocit …

Meaning of retardation. As explained in Section 2.5, the sign of acceleration by itself does not indicate speeding up or slowing down — what matters is the acceleration's direction relative to the instantaneous velocity. When acceleration is directed opposite to the velocity, the body's speed decreases with time; this situation is called retardation, or deceleration, and is conventionally described as a "negative" acceleration once a positive direction has been fixed along the velocity.

The braking car example. Consider a car moving forward (take this as the positive direction) as it approaches a red traffic light. The driver applies the brakes, and the braking force produces an acceleration directed backward — opposite to the car's forward velocity. As long as the car is still moving forward, its velocity remains positive throughout the braking process, while its acceleration is negative (backward) the entire time. Because the acceleration opposes the velocity, the magnitude of the velocity — i.e. the speed — steadily decreases, second by second, until the car finally comes to rest (v = 0) at the light. …

Identify the direction of the car's velocity (forward) and the direction of the braking force/acceleration (backward, opposing the velocity), and ex …

• Assuming 'negative acceleration' always means the body is slowing down, regardless of velocity direction
• Describing the car as moving backward during braking, when in fact it keeps moving forward (at decreasing speed) until it stops …