Final answer:
The impulse required to change the shopping cart's velocity from 3.25 m/s to 7.10 m/s east is calculated based on the impulse-momentum theorem to be 12.52 kg·m/s.
Step-by-step explanation:
The question is about calculating the impulse required to change the velocity of a shopping cart. According to the impulse-momentum theorem, impulse is equal to the change in momentum of the object. The impulse I can be found using the formula I = Δp = m(Δv), where Δp is the change in momentum, m is the mass of the cart, and Δv is the change in velocity.
To solve this problem, we first determine the initial and final momenta. The initial momentum pi is the mass of the cart multiplied by its initial velocity, and the final momentum pf is the mass of the cart multiplied by its final velocity. Then we calculate the change in momentum by subtracting the initial momentum from the final momentum.
Initial momentum, pi = 3.25 kg × 3.25 m/s = 10.56 kg·m/s
Final momentum, pf = 3.25 kg × 7.10 m/s = 23.08 kg·m/s
Change in momentum, Δp = pf - pi = 23.08 kg·m/s - 10.56 kg·m/s
The magnitude of the impulse required is, therefore, Δp = 23.08 kg·m/s - 10.56 kg·m/s = 12.52 kg·m/s.