To find the body's displacement, we're going to stick in our two endpoints for interval S 4 -, s one. So sticking the four into the original S equation minus the one into the original S equation, we're going to get a displacement of -12. Then it says, what's the body's average velocity? And the average velocity is just going to be that -12 the displacement over the time interval, the time interval being 4 -, 1, so -12 / 3 is -4. The next one says what's the body speed at the left and right intervals. So we actually have to find the velocity formula because speed is the absolute value of velocity. So taking the first derivative, we get -32 T to the negative third plus 4T to the negative second. I'm going to go ahead and take the derivative of that to get our acceleration while we're here. So 96 T to the negative 4th -8 T to the negative third. I don't want negative exponents with the variable, so I'm going to rewrite that is -32 / t ^3 + 4 / t ^2 and 96 / t to the 4th -8 / t ^3. So to find the speed, I'm just going to put in V of four and V of one and compute it. And we're going to get 28 and one 4th 28 being at V of one, one fourth being at V of four, the body's acceleration. We're just going to stick in one and four to the acceleration formula and get 88 and one fourth. And then the last one says when, if ever during the interval does the body change direction? Well, if it's changing direction, the velocity equals 0. So if I take this equation and multiply through by the common denominator of t ^3, I'd get 0 equaling -32 + 4 T Add the 32 over, divide by 4 and I get T equal 8. But T equal 8 is not within the given interval of one to four, so the body does not change direction during the interval.