At the local grocery store, you push a 13.9 kg shopping cart. You stop for a moment to add a bag of dog food to your cart. With a force of 12.0 N, you accelerate the cart from rest through a distance of 2.00 m in 3.00 s. What was the mass of the dog food?

Is the cart frictionless?

If so, compute the acceleration a and use
F = m a
to solve for the mass m.

Hint: X = 2.00 m = (1/2) a t^2

To find the mass of the dog food, we need to apply Newton's second law of motion:

F = ma

Where:
F = Force applied (12.0 N)
m = Mass of the dog food (unknown)
a = Acceleration of the cart

To find the acceleration, we can use the following equation:

a = (vf - vi) / t

Where:
vf = Final velocity (will be zero, as the cart starts from rest and stops)
vi = Initial velocity (also zero in this case, as the cart starts from rest)
t = Time taken to accelerate (3.00 s)

Substituting the given values, we get:

a = (0 - 0) / 3.00

Since the acceleration is zero, it means that the cart is not accelerating or decelerating after the force is applied. The dog food only needs to overcome the initial inertia of the cart to start moving.

Now, we can rewrite Newton's second law as:

F = ma

12.0 N = m * 0

The product of mass and acceleration is zero because the acceleration is zero. Therefore, the force only needs to overcome the initial inertia of the cart.

From this, we can understand that the mass of the dog food does not affect the force required to accelerate the cart. It remains at 0 kg, as it is not involved in any acceleration or force calculations. So, the mass of the dog food is 0 kg.