Newton's Laws Graphs
A purely visual and mathematical breakdown of all possible graphs in Newton's Laws of Motion. No general theory—just the exact coordinate systems, slopes, and areas required to solve complex mechanics problems. Designed explicitly for targeted high-yield visual revision.
Force vs Time (F-t) Graph
Visualizing impulsive forces and total change in momentum over a time interval.
The area enclosed under the F-t curve equals the Impulse ($J$), which is exactly the total Change in Momentum ($\Delta p$) delivered to the body.
Momentum vs Time (p-t) Graph
Deriving instantaneous applied force from the rate of change of momentum.
The slope of the tangent at any point on the p-t curve ($\frac{dp}{dt}$) gives the instantaneous Net Force acting on the body at that moment.
Force vs Position (F-x) Graph
Calculating work done by conservative forces like an ideal spring.
A straight line through the origin with negative slope represents a restoring Spring Force ($F = -kx$). The area between the line and the x-axis gives the Work Done, positive on one side and negative on the other.
Friction vs Applied Force (f-F) Graph
The most vital graph for understanding static, limiting, and kinetic friction phases.
Friction matches applied force exactly in the static region (a 45° line, since $f = F$) up to the limiting value $f_{s,max}$, then drops slightly and stays constant at the kinetic value $f_k$.
Acceleration vs Applied Force (a-F) Graph
Mapping how an object accelerates on a rough surface once friction is overcome.
An object on a rough surface doesn't accelerate until the applied Force overcomes friction. The x-intercept marks the kinetic friction $f_k$, and the slope of the rising line equals $1/m$.
Apparent Weight vs Acceleration (Lift Problem)
The single most-asked NLM application graph — a person standing on a weighing machine inside a lift.
Taking upward acceleration as positive, the Normal reaction is $N = m(g + a)$ — a straight line. At $a = 0$ the reading is the true weight $mg$; at $a = -g$ (a snapped cable, free fall) the reading drops to zero, giving true weightlessness.
Acceleration vs 1/Mass (a vs 1/m)
Newton's Second Law re-plotted to isolate mass as a straight-line relationship.
Since $a = F \cdot \frac{1}{m}$ for constant force, plotting $a$ against $1/m$ gives a straight line through the origin. A steeper line means a larger constant force was applied.
Quick Revision Sheet
Formulas explicitly tied to graphing mechanics problems.