How do the signs of velocity and acceleration tell you whether an object is speeding up?
AA negative acceleration always means the object is slowing down
BSame signs mean slowing down, opposite signs mean speeding up
CSame signs mean speeding up, opposite signs mean slowing down
DA positive acceleration always means the object is speeding up
Answer & Solution
Correct answer: C. Same signs mean speeding up, opposite signs mean slowing down
1. Plus and minus signs give the directions of the velocity and the acceleration.
2. If the acceleration has the same sign as the velocity, the object is speeding up.
3. If the acceleration has the opposite sign, the object is slowing down.
4. A negative acceleration will actually increase a negative velocity, so a minus sign alone proves nothing.
5. A positive acceleration slows a negative velocity, so a plus sign alone proves nothing either.
6. Only the pairing of the two signs decides the outcome.
_Source: OpenStax College Physics (CC BY 4.0), Ch 2 "Kinematics", section 2.4 Acceleration_
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