00:01
Here, we're given the graph of a particle's position x of t at a time t, for a region between 0 and 6.
00:10
We're told some details about what we can see here, such as there's a max it and min at 1 and 5, and there's an inflection point at 2.
00:17
We want to know for what values of t is the velocity of the particle increasing.
00:23
So let's call that part a.
00:24
The velocity of the particle will be increasing if it's concave up.
00:31
So if the graph is concave up, it's going to be, the velocity will be increasing.
00:37
And that's going to happen right here, from here until there, because we're told that two is the inflection point.
00:43
So that's going to be from zero to two.
00:46
Now, the next one's a little trickier.
00:49
We want to know for what values of t is the speed of the particle increasing.
00:54
So that's going to happen if the velocity and acceleration are going in the same direction...