Answer:
Part a : Time required for the block to go to 3.05 in is 0.036 s
Part b : Time required for the block to go to 6.1 in is 0.054 s
Explanation:
The acceleration is given as

Here
is the initial acceleration which is given as 420 
- k is the spring constant which is calculated as follows

- Here lc is the compressed length of the spring
- and Iuc is the uncompressed length of the spring so the value of k is

So now the equation becomes

As per relation of acceleration to velocity





Also

So

Solving for dt and integrating results in

Now using this equation value for both parts can be calculated numerically as
Part a 3.05 in

Solving numerically for this value of x

Time required for the block to go to 3.05 in is 0.036 s
Part b 6.1 in

Solving for this value of x

Time required for the block to go to 6.1 in is 0.054 s