Answer
The kinetic energy is at a maximum when the block's position is $~~x = 0.060~m$
Work Step by Step
The block's speed will increase when the magnitude of the applied force is greater than the magnitude of the opposing force on the block by the spring.
The block's speed will reach a maximum when the magnitude of the applied force is equal to the magnitude of the opposing force on the block by the spring.
We can find $x$:
$kx = F$
$x = \frac{F}{k}$
$x = \frac{3.0~N}{50~N/m}$
$x = 0.060~m$
When the speed is at a maximum then the kinetic energy is at a maximum.
The kinetic energy is at a maximum when the block's position is $~~x = 0.060~m$.
