Question

in which case can we say that the rate of change of velocity is negative

Answer 1

when the initial velocity is greater than the final velocity , then we can say that the rate of change of velocity is negative.

Answer 2

When their is rate of change in velocity means acceleration. And when it is in negative it is called retardation.
So, when initial (starting) velocity is greater and final velocity is smaller then it will be in negative.
Eg:u=12and v=8 and t=2then a=v-u/t
=8-12/2
=-2
Therefore in negative
Hence proved..
Hope u like it