Newton-Second

The newton-second ($\mathrm{N}\mathrm{s}$) is the derived SI unit for Impulse and Momentum.

Impulse is force applied over time:

$$J_{imp}=F\Delta t$$

Momentum is mass times velocity:

$$p=mv$$

The units match:

$$\mathrm{N}\mathrm{s}=(\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-2})\mathrm{s}=\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$$

and

$$\mathrm{kg}(\mathrm{m}{\mathrm{s}}^{-1})=\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$$

This equality is the unit-level version of the impulse-momentum theorem:

$$F\Delta t=\Delta p$$

Example: if a $10\mathrm{N}$ force acts for $0.5\mathrm{s}$, the impulse is:

$$10\mathrm{N}\times 0.5\mathrm{s}=5\mathrm{N}\mathrm{s}$$

so the object’s momentum changes by $5\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$.

Andrew-friendly intuition: a big force for a short time and a small force for a long time can produce the same momentum change. This is why padding, crumple zones, and bending your knees reduce peak force: they stretch the collision time for roughly the same impulse.

Common mistake: impulse is not the same as force. It includes how long the force acts, which is why its unit contains seconds.

Quick check

Newton-seconds are impulse units, but they are equivalent to momentum units:

$$1\mathrm{N}\mathrm{s}=1\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}.$$

That equality is the whole impulse-momentum theorem in unit form: force applied over time changes momentum.

Common use

Use newton-seconds when a force acts for a short time, like a collision, bat hit, kick, or rocket thrust interval. The detailed force may vary, but the area under the force-time graph gives the impulse.