180 J

To calculate the work done by the force, we can use the formula:

Work = force x distance x cos(theta)

where force is the retarding force, distance is the distance traveled while the force is acting, and theta is the angle between the force and the direction of motion.

In this case, we know the initial and final velocities of the body, so we can calculate the change in velocity:

Change in velocity = final velocity - initial velocity
= 2 ms^-1 - 5 ms^-1
= -3 ms^-1

Since the body is slowing down, the direction of the force is opposite to the direction of motion, so theta = 180 degrees. We also know the mass of the body, so we can calculate the force using Newton's second law:

force = mass x acceleration

The acceleration is given by:

acceleration = (final velocity - initial velocity) / time taken

We don't know the time taken, but we can use the fact that the body is slowing down to write:

time taken = distance / average velocity

where distance is the distance traveled while the force is acting, and average velocity is the average of the initial and final velocities:

average velocity = (final velocity + initial velocity) / 2
= (2 ms^-1 + 5 ms^-1) / 2
= 3.5 ms^-1

We can solve for distance using the formula:

distance = average velocity x time taken

Substituting the expressions for time taken and average velocity, we get:

distance = (final velocity - initial velocity) x mass / acceleration
= (-3 ms^-1) x (20 kg) / ((2 ms^-1 - 5 ms^-1) / time taken)
= 60 m

Now we can calculate the force:

force = mass x acceleration
= (20 kg) x ((2 ms^-1 - 5 ms^-1) / time taken)
= (20 kg) x (-3 ms^-2 / (60 m / (3 ms^-1)))
= -30 N

The negative sign indicates that the force is in the opposite direction to the motion of the body.

Finally, we can calculate the work done by the force:

Work = force x distance x cos(theta)
= (-30 N) x (60 m) x cos(180 degrees)
= -1800 J

The negative sign indicates that the work done by the force is negative, which means that the force is doing work against the motion of the body. To get the magnitude of the work done, we can take the absolute value:

|Work| = 1800 J

Therefore, the work done by the retarding force is 180 J.