Answer all parts with step by step calculation

An air parcel initially at rest is subjected to a constant pressure gradient force in the x direction, as it accelerates over some distance x during a time interval t. Write the relationship between force and acceleration for this problem, considering only the pressure gradient force for now. Assume pressure only varies in the x direction and does not change in time. (a) Integrate the equation to solve for the parcel's u velocity at the end of t. (b) Then come up with a way to write t in terms of x and use this expression to solve for u in terms of the pressure difference over the distance traveled. (c) Assuming the pressure difference is 4 hPa, estimate the value of u. (d) If pressure increases in the x direction, what is the sign of the u wind component? Hint: If you're really stuck, you could try a different approach to find u by thinking about the kinetic energy of the parcel and the work done by the pressure gradient force.