Does Constant Acceleration Always Change Velocity's Magnitude?

[mohabitar]

The magnitude of the velocity of an object must change if the magnitude of its acceleration is a constant. True or false?

I chose true, however the correct answer is false. Here's my reasoning: If acceleration is constant, that means velocity is linear. If velocity is linear, that means it's magnitude is increasing.

Where did I go wrong here?

 

[SEngstrom]

consider the velocity and acceleration of an object in a steady circular orbit for a counterexample to your reasoning.

 

[MysticDude]

What if the velocity is constant?

 

[mohabitar]

Then acceleration is zero

 

[MysticDude]

The acceleration also has a constant of zero.

 

[spyrustheviru]

velocity is a vector and it is defined by it's magnitude and direction-should any of these change, we say that velocity changes. When you have a non zero acceleration,velocity will surely change, but since it is a vector it doesn't have to be it's magnitude that changes. circular orbit is indeed a very good example.

 

[mohabitar]

Well if its not its magnitude, then what changes? Direction?

 

[SEngstrom]

To take the example of a steady circular orbit (e.g. Earth around the Sun) - the Earth is held in the orbit by acceleration that is directed towards the Sun but has a constant amplitude. The velocity vector changes but again its amplitude is constant.

Since you only have to provide one counterexample to disprove the original statement, another answer would be a=0, v=const, but only because of a little slop in the problem formulation IMHO :-)