A shopper in a supermarket pushes a loaded 36 kg cart with a horizontal force of 12 N.

(a) How far will the cart move in 3.5 s, starting from rest? (Disregard friction.)
(b) How far will the cart move in 3.5 s if the shopper places an 95 N child in the cart before pushing?

To find the distance the cart moves in both scenarios, we can use the equation for calculating displacement:

Displacement = (initial velocity * time) + (0.5 * acceleration * time^2)

Given that the initial velocity is zero (since the cart starts from rest) and that there is no friction to consider, the only force acting on the cart is the force applied by the shopper.

(a) In the first scenario, where the cart has a weight of 36 kg and a horizontal force of 12 N is applied for 3.5 seconds, we can calculate the distance the cart will move.

Step 1: Calculate acceleration.
Since the only force acting on the cart is the applied force, we can use Newton's second law to find the acceleration:

Force = mass * acceleration

Rearranging the equation, we get:

acceleration = force / mass

acceleration = 12 N / 36 kg

acceleration = 0.33 m/s^2

Step 2: Calculate displacement.
Using the equation for displacement, we have:

Displacement = (0 * 3.5) + (0.5 * 0.33 * 3.5^2)

Displacement = (0) + (0.5 * 0.33 * 12.25)

Displacement = (0) + (0.5 * 3.925)

Displacement = 1.9625 meters

Therefore, in 3.5 seconds, the cart will move approximately 1.9625 meters.

(b) In the second scenario, where the shopper places a child weighing 95 N in the cart before pushing, we need to consider the additional force exerted on the cart.

Step 1: Calculate net force.
We need to add the force exerted by the child to the horizontal force applied by the shopper:

Net force = force applied by shopper + force exerted by child

Net force = 12 N + 95 N

Net force = 107 N

Step 2: Calculate acceleration.
Using Newton's second law again, rearranging the equation, we have:

acceleration = net force / mass

acceleration = 107 N / 36 kg

acceleration = 2.97 m/s^2

Step 3: Calculate displacement.
Using the equation for displacement, we have:

Displacement = (0 * 3.5) + (0.5 * 2.97 * 3.5^2)

Displacement = (0) + (0.5 * 2.97 * 12.25)

Displacement = (0) + (0.5 * 36.2425)

Displacement = 18.12125 meters

Therefore, in 3.5 seconds, with the additional weight of the child, the cart will move approximately 18.12125 meters.