Question

Is it true that constant velocity means zero acceleration but constant acceleration does not mean zero velocity?

Answer 1

True (both)

Explanation:

Acceleration is defined as the change in velocity over time:

`a=(Deltav)/(Deltat)or (dv)/(dt)`

If there is no change in velocity (`Deltav=0`) then the acceleration `=0`

If acceleration is constant, then the velocity will change by a constant amount every second, in other words: velocity is NOT constant.

Example:
Velocity is constant `v=5m//s`
Then acceleration `a=(Deltav)/t=0/t=0`

Example2:
Acceleration is constant, let's say `a=1m//s^2`
Then `v_1=v_0+1m//s`, `v_2=v_0+2m//s`, etc.

Example3:
We start with an initial velocity of `v=5m//s` and a negative acceleration of `a=-1m//s^2` (as in braking):
Then after 5 seconds velocity will be `=0`, but then the braking is over (so `a!=-1` anymore).