Final answer:
The mass of the groceries in the cart is approximately 10.7 kg. This is found by first calculating the acceleration of the cart and then using Newton's second law to solve for the combined mass of the cart and groceries, followed by subtracting the mass of the cart.
Step-by-step explanation:
To determine the mass of the groceries in the cart, we must first calculate the acceleration of the cart and then use Newton's second law of motion. Since friction is ignored, we can apply the formula a = F/m, where a is the acceleration, F is the force, and m is the total mass (cart + groceries).
First, we find the acceleration of the cart using the formula derived from the equations of motion: a = 2s/t², where s is the distance traveled and t is the time. Substituting the given values, we get a = (2 * 3.5 m) / (5.0 s)² = 0.28 m/s².
Now, applying Newton's second law and substituting the total force and acceleration, we can solve for the combined mass of the cart and groceries: 10 N = (25kg + m_{groceries}) * 0.28 m/s². To find the mass of the groceries, rearrange the equation: m_{groceries} = 10 N / 0.28 m/s² - 25 kg. Thus, the mass of the groceries is approximately 10.7 kg.