AP® Physics 1: Algebra-Based · Unit 1 · Topic 1.2
Acceleration and the Sign Trap
An object speeds up when acceleration and velocity point the same direction, and slows down when they point opposite directions. The sign of acceleration alone never tells you which.
Acceleration is just the rate velocity changes, a = delta v / delta t. It doesn't care which way is 'positive' in some absolute sense, only which way you chose as positive for your problem. That choice makes the same physical situation look different on paper: a ball thrown downward has negative velocity and negative acceleration, while a car moving in the negative direction but braking has positive acceleration and negative velocity. Both describe real, sensible motions.
The rule that actually matters: compare the sign of acceleration to the sign of velocity. Same sign means they're pulling the same way, so speed increases. Opposite signs mean acceleration is fighting the motion, so speed decreases. This is why a ball thrown straight up is still accelerating at the very top of its path, even though its velocity is zero there for an instant. Gravity never switches off; the acceleration stays constant at -9.8 m/s2 the whole flight, it's only the velocity that passes through zero on its way from positive to negative.
This sign logic is what makes the three motion graphs consistent with each other. On a velocity-time graph, the slope is acceleration; where that slope and the velocity curve share a sign, the object speeds up, and where they disagree, it slows down. Keep this straight before moving to projectiles, where the vertical velocity reverses sign exactly like the ball above while acceleration from gravity never changes.
Key terms
- Acceleration
- The rate at which velocity changes, equal to delta v divided by delta t.
- Sign convention
- The choice of which direction counts as positive for a given problem.
- Speeding up
- Occurs when acceleration and velocity have the same sign, so they point the same direction.
- Slowing down
- Occurs when acceleration and velocity have opposite signs, so acceleration opposes the motion.
Watch it explained
- How it worksHow do the signs of velocity and acceleration together decide whether something speeds up or slows down?
- Common mistakeWhy doesn't a negative acceleration always mean an object is slowing down?
- Worked exampleFind the acceleration of a car that drops from 28 m/s to 12 m/s in 4 seconds.
- Going furtherWhat does the motion look like when acceleration stays constant while velocity passes through zero?
Check yourself
End of topic.