Physics question

Question

1) I know that acceleration is the change in velocity. So does even the slightest change in acceleration mean that there was a slight change in velocity?

2) Also, on a velocity vs. time graph, how do I draw two velocities, one with positive slope and the other with negative slope, yet they both would result to a negative acceleration? Is this possible?

Answer 1

1) No, the amount of any acceleration change has no bearing on change of velocity.

Change in velocity is the MAGNITUDE of acceleration, and is independent of CHANGE in acceleration.

2) It is impossible.

The slope of (the tangent to) the velocity curve IS the acceleration.