Where c is a constant that depends on the initial gas pressure behind the projectile. The initial position of the projectile is s=1.5m and the projectile is initially at rest. The projectile accelerates until it reaches the end of the barrel at s=3m. What is the value of the constant c such that the projectile leaves the barrel with a velocity of 200 m/s?

Complete Question

A gas gun uses high pressure gas tp accelerate projectile through the gun barrel.

If the acceleration of the projective is : a = c/s m/s2

Where c is a constant that depends on the initial gas pressure behind the projectile. The initial position of the projectile is s= 1.5m and the projectile is initially at rest. The projectile accelerates until it reaches the end of the barrel at s=3m. What is the value of the constant c such that the projectile leaves the barrel with velocity of 200m/s?

The value of the constant is  

Explanation:

From the question we are told that

         The acceleration is  

         The  initial position of the projectile is s= 1.5m

         The final position of the projectile is

          The velocity is  

     Generally  

   and  acceleration is

so

 =>        

integrating both sides

Now for the limit

          a =  200 m/s

             b = 0 m/s  

         c = s= 3 m

          d == 1.5 m

So we have  

=>