Impulse of the force:
The impulse of a force is defined as the change in momentum caused by that force. The impulse-momentum theorem states that the impulse of a force is equal to the change in momentum of an object.

The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the hammer is 1 kg and its initial velocity is 6 m/s.

Therefore, the initial momentum of the hammer is:

P_initial = mass × velocity = 1 kg × 6 m/s = 6 kg·m/s

When the hammer strikes the wall, it comes to rest. This means its final velocity is 0 m/s. The final momentum of the hammer is:

P_final = mass × final velocity = 1 kg × 0 m/s = 0 kg·m/s

The change in momentum is then:

ΔP = P_final - P_initial = 0 kg·m/s - 6 kg·m/s = -6 kg·m/s

Thus, the impulse of the force exerted on the hammer is -6 kg·m/s.

Average retarding force:
The average retarding force can be calculated using the impulse-momentum theorem and the time taken for the hammer to come to rest.

The impulse of a force is given by the product of the force and the time interval over which it acts. Therefore, we can write:

Impulse = force × time

Rearranging the equation, we have:

Force = Impulse / time

In this case, the impulse of the force is -6 kg·m/s and the time taken for the hammer to come to rest is 0.1 s. Plugging in these values, we get:

Force = -6 kg·m/s / 0.1 s = -60 N

The negative sign indicates that the force is acting in the opposite direction of the initial motion of the hammer. Therefore, the average retarding force that stops the hammer is -60 N.

Average retardation:
The average retardation of the hammer can be calculated using the formula:

Average retardation = Change in velocity / Time taken

In this case, the change in velocity is the final velocity (0 m/s) minus the initial velocity (6 m/s), and the time taken is 0.1 s.

Average retardation = (0 m/s - 6 m/s) / 0.1 s = -60 m/s²

The negative sign indicates that the retardation is in the opposite direction of the initial velocity. Therefore, the average retardation of the hammer is -60 m/s².

Summary:
a) The impulse of the force exerted on the hammer is -6 kg·m/s.
b) The average retarding force that stops the hammer is -60 N.
c) The average retardation of the hammer is -60 m/s².

The negative sign in both the force and retardation indicates that they are acting in the opposite direction of the initial motion of the hammer.