Complete science reading
Impulse is a change in momentum
For one body, net impulse J_net=Δp=m(v_final−v_initial) when mass remains constant. Its direction matters. A 1.5 kg cart slowing from +4 m/s to 0 has Δp=1.5(0−4)=−6 N·s. This negative sign indicates impulse to the left in a right-positive coordinate system.
A force sustained over time
When net force is constant during a duration Δt, J_net=F_netΔt. If force varies, impulse is the signed area under the net force-versus-time curve: J_net=∫F_net dt. The mean net force over the duration is J_net/Δt. Do not substitute one moment's force for average force without justification.
A longer interaction can reduce average force
Suppose a chosen body must undergo Δp=−12 N·s. Spread across 0.20 s, its mean net force is −60 N. Spread across 0.60 s, its mean is −20 N. Same signed impulse, one-third the average-force magnitude in the longer case. A softer contact is not intrinsically proven safer by this numerical comparison; real force distributions and injuries depend on more factors.
Force and work are not interchangeable
Impulse uses force times time and changes momentum; work uses force along displacement and changes kinetic energy when summed across forces. A force perpendicular to velocity can change direction and momentum while doing no instantaneous work. The digital studies model prescribed one-dimensional impulse rather than realistic collisions.