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

1 Answer
MeneerNask
May 30, 2018

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).

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