# Velocity increase while acceleration decrease?

I'm having trouble understanding velocity and acceleration.

Is it possible for velocity to be increasing while acceleration decreases and vice versa?

• Let $v(t)=-1/t$; then $a(t)=1/t^2$. $v$ is increasing and $a$ is decreasing. Change sign of $v$ and...? – Michael Galuza Aug 4 '15 at 10:41

Since acceleration $a$ is deferential of velocity $v$, so as Michael pointed out it is possible to have a situation that $v >0$ while $a = dv/dt < 0$.
Acceleration is the rate of change of velocity defined by $a=dv/dt$, so even if acceleration is decreasing as long as it is positive it velocity would increase. So if for example at time $t=0$ we have that $a=2m/sec^2$ which means that every second the velocity increases by 2 m/sec , and then say at time $t=1$ we have $a=1 m/sec^2$ i.e $da/dt<0$ we still have that the velocity would increase by $1m/sec$ You can argue for the second part of your question similarly. I hope this helps.