Does negative acceleration always mean slowing down?
Short answer: It speeds up when v and a have the same sign, whatever that sign is.
The trap
The wrong idea
“Negative acceleration always means the object is slowing down.”
It sounds reasonable, and a lot of JEE aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
An object has v = -5 m/s and a = -2 m/s². It is:
- Slowing down
- Speeding up
- At constant speed
Show the answer
B. Speeding up
It speeds up when v and a have the same sign, whatever that sign is.
The click
The sign of acceleration only tells you its direction along the axis you chose. Whether an object speeds up or slows down depends on how its acceleration compares with its velocity.
The rule: if v and a have the same sign (point the same way), speed increases. If they have opposite signs, speed decreases. Here v = −5 m/s and a = −2 m/s². Both point in the negative direction, so after 1 s, v = −5 + (−2)(1) = −7 m/s. The speed went from 5 m/s to 7 m/s: the object is speeding up.
A concrete picture: take "up" as positive and drop a ball. Its velocity is negative (downward) and its acceleration is −g (downward). It obviously speeds up as it falls, even though its acceleration is "negative".
The word deceleration means slowing down, that is, acceleration opposite to velocity. That is not the same as negative acceleration. If you flip your axis, every sign flips, but the physics (speeding up or slowing down) stays the same, which proves the sign alone can't decide it. A quick test: speed is increasing when v·a > 0 and decreasing when v·a < 0.
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