# How do you find values of t in which the speed of the particle is increasing if he position of a particle moving along a line is given by #s(t)=2t^3-24t^2+90t+7# for #t≥0#?

##### 1 Answer

Feb 17, 2015

If

The speed (at time t) is given by

Acceleration is given by the second derivative

Critical point for acceleration (when the speed changes from decreasing to increasing) occurs when

That is when

This might be easier to see if we consider a table of time(t) and speed at time t:

We can see that the speed actually decreases until somewhere between