The same change, spread over time.

Momentum p = mv is a vector. Impulse is the change in momentum and equals the signed area under a force–time graph. For a constant or average net force, impulse is FΔt.

Total momentum is conserved when the net external impulse is negligible. In an inelastic collision kinetic energy decreases while total energy remains conserved. Extending stopping time reduces average force for the same momentum change.

INTERACTIVE MODEL

Same impulse, different force

Impulse magnitude / N s12

READ THE GRAPH

Explore the relationship

Compare average force for a fixed momentum change; the actual force can vary during contact.

Average force magnitude / N

Tap or focus a plotted point to read its values.

View plotted data as a table

Explore the relationship
Series	Stopping time / s	Average force magnitude / N
Average force magnitude / N	0.1	120
Average force magnitude / N	0.115	104.348
Average force magnitude / N	0.13	92.3077
Average force magnitude / N	0.145	82.7586
Average force magnitude / N	0.16	75
Average force magnitude / N	0.175	68.5714
Average force magnitude / N	0.19	63.1579
Average force magnitude / N	0.205	58.5366
Average force magnitude / N	0.22	54.5455
Average force magnitude / N	0.235	51.0638
Average force magnitude / N	0.25	48
Average force magnitude / N	0.265	45.283
Average force magnitude / N	0.28	42.8571
Average force magnitude / N	0.295	40.678
Average force magnitude / N	0.31	38.7097
Average force magnitude / N	0.325	36.9231
Average force magnitude / N	0.34	35.2941
Average force magnitude / N	0.355	33.8028
Average force magnitude / N	0.37	32.4324
Average force magnitude / N	0.385	31.1688
Average force magnitude / N	0.4	30
Average force magnitude / N	0.415	28.9157
Average force magnitude / N	0.43	27.907
Average force magnitude / N	0.445	26.9663
Average force magnitude / N	0.46	26.087
Average force magnitude / N	0.475	25.2632
Average force magnitude / N	0.49	24.4898
Average force magnitude / N	0.505	23.7624
Average force magnitude / N	0.52	23.0769
Average force magnitude / N	0.535	22.4299
Average force magnitude / N	0.55	21.8182
Average force magnitude / N	0.565	21.2389
Average force magnitude / N	0.58	20.6897
Average force magnitude / N	0.595	20.1681
Average force magnitude / N	0.61	19.6721
Average force magnitude / N	0.625	19.2
Average force magnitude / N	0.64	18.75
Average force magnitude / N	0.655	18.3206
Average force magnitude / N	0.67	17.9104
Average force magnitude / N	0.685	17.5182
Average force magnitude / N	0.7	17.1429
Average force magnitude / N	0.715	16.7832
Average force magnitude / N	0.73	16.4384
Average force magnitude / N	0.745	16.1074
Average force magnitude / N	0.76	15.7895
Average force magnitude / N	0.775	15.4839
Average force magnitude / N	0.79	15.1899
Average force magnitude / N	0.805	14.9068
Average force magnitude / N	0.82	14.6341
Average force magnitude / N	0.835	14.3713
Average force magnitude / N	0.85	14.1176
Average force magnitude / N	0.865	13.8728
Average force magnitude / N	0.88	13.6364
Average force magnitude / N	0.895	13.4078
Average force magnitude / N	0.91	13.1868
Average force magnitude / N	0.925	12.973
Average force magnitude / N	0.94	12.766
Average force magnitude / N	0.955	12.5654
Average force magnitude / N	0.97	12.3711
Average force magnitude / N	0.985	12.1827
Average force magnitude / N	1	12

Probe along the horizontal axis0.1Average force magnitude / N: 120

Explore: Keep impulse fixed while increasing stopping time. Compare average force.

p=mv\qquad J=\Delta p=F_{\rm av}\Delta t

WORKED EXAMPLE

A 2 kg cart at 3 $\mathrm{m}\,\mathrm{s}^{-1}$ sticks to a stationary 1 kg cart.

Initial momentum = 6 kg $\mathrm{m}\,\mathrm{s}^{-1}$ .
Common velocity = 6/(2 + 1) = 2 $\mathrm{m}\,\mathrm{s}^{-1}$ .

Assumed knowledge

Net force and signed velocity.

Learning checkpoints & source

YOUR LEARNING CHECKPOINT

Relate impulse to momentum change.
Apply momentum conservation in one dimension.

QCAA Physics · Unit 2 · Linear motion and force ↗

READY TO TRY IT?

The same change, spread over time.

Same impulse, different force

Explore the relationship

A 2 kg cart at 3 m s−1\mathrm{m}\,\mathrm{s}^{-1}ms−1 sticks to a stationary 1 kg cart.

Put the idea to work.

A 2 kg cart at 3 $\mathrm{m}\,\mathrm{s}^{-1}$ sticks to a stationary 1 kg cart.