a(t) = 2t + 5,    s(0) = 7,    v(0) = −9

It seems like you're asking for help with a physics problem involving motion, but you haven't provided a specific question. The given information includes an acceleration function a(t) = 2t + 5, an initial position s(0) = 7, and an initial velocity v(0) = -9.

Here's a general approach to problems like this:

1. Integrate the acceleration function to find the velocity function. The integral of a(t) = 2t + 5 is v(t) = t^2 + 5t + C, where C is the constant of integration.

2. Use the initial condition v(0) = -9 to solve for C. Substituting these values into the velocity function gives -9 = 0 + 0 + C, so C = -9. Therefore, the velocity function is v(t) = t^2 + 5t - 9.

3. Integrate the velocity function to find the position function. The integral of v(t) = t^2 + 5t - 9 is s(t) = (1/3)t^3 + (5/2)t^2 - 9t + D, where D is another constant of integration.

4. Use the initial condition s(0) = 7 to solve for D. Substituting these values into the position function gives 7 = 0 + 0 - 0 + D, so D = 7. Therefore, the position function is s(t) = (1/3)t^3 + (5/2)t^2 - 9t + 7.

Please provide a specific question if you need more help!