Kinetic energy is a form of energy that an entity or particle possesses due to its motion.

The relation between the object's mass and its speed.

KE = \frac{1}{2} mv^2

The work done is equal to the product of the applied force's magnitude and the distance traveled by the body.

W = f d

Step 1: Calculate the work done by the cart

Given that

Mass of the shopping cart m = 20kg

Shopping cart initial speed v_i = 4 m/s

Friction force f_f = 4N

Initial kinetic energy KE_i = \frac{1}{2}mv_i^2     

KE_i = \frac{1}{2} (20kg)(4 m/s)^2

KE_i = 160 kg m^2/s^2

Thus, Initial kinetic energy KE_i = 160 joules

Since the cart will come to a complete stop, the final kinetic energy will be zero.

Final kinetic energy KE_f = 0

The change in kinetic energy is equivalent to work.

Change in kinetic energy \Delta KE=KE_f-KE_i

\Delta KE = 0 - 160

Work done W = \Delta KE = - 160 joules

"-" shows opposite direction of motion

Work done W = 160 joules

Step 2: Measure the cart's distance traveled until it came to a halt.

Work done W = f_f * d

160 joules = 4 N* d

d = \frac{160 joules}{4N}

d = 40 meters

Hence, The cart's total distance traveled before coming to a stop, d = 40 meters