Answer:
Force constant will be 1195.85 N/m
Work done will be 1.6859 J
Explanation:
We have given the force, F = 63.5 N
Spring is stretched by 5.31 cm
So x = 0.0531 m
Force is given , F = 63.5 N
We know that force is given by 
So 
k = 1195.85 N/m
Now we have to find the work done
We know that work done is given by

here we will use the concept of Newton's III law
as per Newton's III law the impulse given to the ball is same as the impulse lost by the bat
So here we will say
impulse gain by the ball = impulse lost by the bat

given that


For ball the change in speed will be

now from above equation


so speed of bat will decrease by 6.72 mph
Since, F = k . ∆x
Therefore, k = F / ∆x = 250 / 0.2 = 1250 N/m
(ps: convert 20 cm into 0.2 m)