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Rearranging the relationship between force, change in momentum, and time by dividing both sides by Δt\Delta t tells us that the net force acting on an object is equal to the rate of change of its linear momentum:

Fnet=ΔpΔt\vec{F}_\text{net}=\frac{\Delta \vec{p}}{\Delta t}

In one dimension, on a graph where the vertical axis represents momentum pp and the horizontal axis represents time tt, the term ΔpΔt\frac{\Delta p}{\Delta t} corresponds mathematically to the slope of the line. Therefore, the physical quantity of net force is determined by finding the slope of the momentum-time graph.

To calculate the net force during a time interval where the graph forms a straight line, one determines the slope of that linear segment. For a segment defined by an initial point (ti,pi)(t_i, p_i) and a final point (tf,pf)(t_f, p_f), the net force is calculated as the change in momentum (rise) divided by the change in time (run):

Fnet=slope=pfpitftiF_\text{net} = \text{slope} = \frac{p_f - p_i}{t_f - t_i}

If the graph is linear, the slope is constant, indicating that a constant net force is acting on the object throughout that duration.

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