Final answer:
The magnitude of the impulse required to change the velocity of a 3.25kg shopping cart from 3.25 m/s to 7.10 m/s east is 12.5125 kg·m/s.
Step-by-step explanation:
The question pertains to the application of the impulse-momentum theorem in physics, which states that impulse is equal to the change in momentum. To find the magnitude of the impulse required to change the shopping cart's velocity from 3.25 m/s to 7.10 m/s east, we first calculate the change in momentum. The change in momentum (Δp) is given by Δp = m × Δv, where m is the mass of the cart and Δv is the change in velocity.
Given that the mass of the cart is 3.25 kg and the change in velocity is Δv = (7.10 - 3.25) m/s = 3.85 m/s, we can calculate the change in momentum as:
Δp = 3.25 kg × 3.85 m/s = 12.5125 kg·m/s.
The magnitude of the impulse required to achieve this change in velocity is thus 12.5125 kg·m/s. Remember that the direction of the impulse would be the same as the direction of the change in velocity, which is east in this case.