First Order Differential Equations: Separable Equations and Applications

I please need your help with the following homework problems. I want to make sure that I followed the correct procedure in solving these problems. Thanks!

1. Solve the Initial Value Problem:

a) dy/dx= (x)^1/2, y(4)= 0

b) dy/dx= cos 2x, y(0)= 1

c) dy/dx= xe^(-x), y(0)=1

2. A moving particle has acceleration a(t)=5, intial velocity v=1, and initial position x=2. Find the position function x(t) of the particle.

3. A moving particle has acceleration a(t)= 2t+1, initial velocity v=-7, and initial position x=4. Find the position function x(t) of the particle.

4. The skid marks made by an automoblie indicated that its brakes were fully applied for a distance of 75m before it came to a stop. The car in quesion is known to have a constant deceleration of 20 m/s^2 under these conditions. How fast - in km/h - was the car traveling when the brakes were first applied?