What is the impulse delivered to an object when a constant force F is applied for time Δt?

What is the impulse delivered to an object when a constant force F is applied for time Δt?

• A. Δp = F / Δt
• B. Δp = F × Δt
• C. Δp = F × Δt / m
• D. Δp = Δt / F

Answer: (B)

Impulse is the change in momentum produced by a force over a time interval. When a constant force F acts on an object for a time Δt, the momentum of the object changes by an amount Δp = F Δt. This is the impulse—the area under the force-versus-time graph for that interval—and it matches the units: newton-seconds, which are equivalent to kilogram meters per second, the units of momentum. Why this form fits: multiplying the constant force by the duration gives exactly how much momentum is delivered during that interval. The other expressions don’t align with the physical meaning or the units. Dividing by time would give something with units of force per time, not momentum. Including a division by mass would yield a velocity change, not a momentum change. And taking the reciprocal of force with time has no correct physical interpretation for impulse.

Impulse is the change in momentum produced by a force over a time interval. When a constant force F acts on an object for a time Δt, the momentum of the object changes by an amount Δp = F Δt. This is the impulse—the area under the force-versus-time graph for that interval—and it matches the units: newton-seconds, which are equivalent to kilogram meters per second, the units of momentum.

Why this form fits: multiplying the constant force by the duration gives exactly how much momentum is delivered during that interval. The other expressions don’t align with the physical meaning or the units. Dividing by time would give something with units of force per time, not momentum. Including a division by mass would yield a velocity change, not a momentum change. And taking the reciprocal of force with time has no correct physical interpretation for impulse.