We're given that S equal negative t ^3 plus fifteen t ^2 -, 72 T so the velocity is the first derivative or -3 T squared plus thirty t -, 72. The acceleration is the derivative of velocity or -6 T plus 30. So the first question says what's the body's acceleration each time the velocity is 0? So we're going to set the velocity equal to 0 and we're going to solve and I personally, I'm going to divide everything through by three and get 0 equal actually negative three t ^2 -, 10 T plus 24. And that probably is easier to see that that factors. So we get 0 equaling t - 4 * t - 6. So we know T equal 4 and t = 6 to make the velocity 0. But it's asking what the body's acceleration is when the velocity is 0. So now we want a of four -6 * 4 + 30 -6 * 4 negative 24 + 30 is 6. And I also want a of six, so -6 * 6 + 30 negative 36 + 30 negative 6. The next part says what's the body speed each time the acceleration is 0. So now we're going to set the acceleration equal to 0 next 0 equal -6 T plus 30. So 6 T equal 30 T equal 5. From there we're going to stick that into the velocity equation. But we have to have the absolute value because we want the speed. So I need the absolute value of V of five negative 3 * 5 ^2 + 30 * 5 - 72. So -3 * 25 is -75 + 150 - 72. So that's going to give me 75 -, 72 or three. Now the last part says, what's the total distance traveled from traveled by the body from zero to five? Well, we need to come back here and realize when velocity is 0, we're changing direction. So we need to figure out S of 4 -, s of 0 and we're going to take the absolute value of that because it's a distance traveled and I don't know why my pins not working well. OK, S of 4 -, s of 0. And then we're going to also find the absolute value of S of 5 -, s of four. So to get the S of four, we're literally going to just stick 4IN here and -4 ^3, it's going to be -64 4 ^2 1616 * 15. That's going to give us 240 4 * 72 so -288 and when I put zero in, those are all going to be 0. So the absolute value of that so -64 + 240 -, 288, the absolute value is 112. So now we're going to do S of 5 -, s of 4. Oops, this one was S of 0. Trying to make it so it's more legible. Sorry. OK. So S of five, we're going to stick 5 in there and we're going to get -5 or negative of five cubes to -125 plus 15 * 25375 -15 no -5 * 72. And then that's all minus the s s of four, which we found a minute ago. The S of four was negative 112 because we're subtracting it before we take the absolute value. So -125 + 375 -, 360 + 112 is going to give us out too. So the total distance traveled is 112 + 2.