An unstretched spring has a length of 10cm when the spring is stretched by a force of 16 newtons it's length is increased to 18 cm what is the spring constant of the spring

Hook's law states that the relationship between the force F applied to a spring and the elongation/compression  of the spring (with respect to its equilibrium position) is

where k is the spring constant, and the negative sign simply means that the direction of the force is opposite to the displacement.

In our problem, the spring is stretched by

And so we can use Hook's law to find the spring constant (we can ignore the sign and consider only the magnitude of the force, 16 N):