A $250g$ particle is subjected to a constant force of $4N$ for $3s$. What is the magnitude of the impulse delivered to the particle by the force?

• A. $0.75N\cdot s$
• B. $0.012N\cdot s$
• C. $83.3N\cdot s$
• D. $12N\cdot s$

Answer: (D)

Verified step by step guidance

1. Identify the given quantities: mass \(m = 250\ \text{g} = 0.250\ \text{kg}\) (convert grams to kilograms), force \(F = 4\ \text{N}\), and time interval \(\Delta t = 3\ \text{s}\).
2. Recall the definition of impulse \(J\), which is the product of the force applied and the time interval during which it acts: \(J = F \times \Delta t\)
3. Substitute the known values into the impulse formula: \(J = 4\ \text{N} \times 3\ \text{s}\)
4. Calculate the product to find the magnitude of the impulse (do not compute the final number here, just set up the expression).
5. Interpret the result: the impulse has units of Newton-seconds (\(\text{N} \cdot \text{s}\)) and represents the change in momentum of the particle due to the applied force.