Read impulse from a force–time graph
You will be able to: Calculate signed impulse and average force from simple force–time shapes.
What does the area of a force pulse tell us?
A push that rises from zero to 8 N and returns to zero over 2 s forms a triangle on a force–time graph. It changes momentum by 8 N·s, just like a steady 4 N push lasting 2 s.
A useful starting point: Impulse: explain a stop or a rebound →
Words and symbols before equations
- Horizontal axis
- Elapsed time in seconds (s).
- Vertical axis
- Signed net force along the chosen axis, in newtons (N).
- Signed area
- Area above zero is positive; below zero is negative.
- Peak force
- Largest force magnitude during the interval, not generally the average.
What this picture assumes
Ideal net-force pulse along one axis. Triangle starts/ends at zero; rectangle stays at the selected force. Area is signed. Shape selection changes the force history, not the mass.
Connect the picture to the physics
For a rectangle, impulse equals height times width: FΔt. A triangular pulse has half the area of its surrounding rectangle: J=½F_peak Δt. The area units are N×s, the units of impulse.
Break more complicated graphs into rectangles, triangles or trapezoids. Add their signed areas. If force switches sign, positive and negative contributions can partly or fully cancel.
Average force is the total signed area divided by duration. A triangle from 0 to 8 N back to 0 over 2 s has J=8 N·s and F_avg=4 N. Graph height alone does not determine impulse; duration matters too.
A worked example, step by step
A net force is +6 N for 2 s, then −2 N for 1 s. An object starts with p_i=+3 kg·m/s. Find the total impulse and final momentum.
- First rectangle: J_1=(6)(2)=+12 N·s.
- Second rectangle: J_2=(−2)(1)=−2 N·s.
- J_net=12−2=+10 N·s; p_f=p_i+J=3+10=+13 kg·m/s.
- Over all 3 s, F_avg=10/3≈3.33 N. It differs from both force levels.
Area below the time axis must subtract. Using peak force as the average overestimates a triangular pulse by a factor of two.
Two pulses have equal signed areas but different shapes. Is their impulse equal?
Compare with an explanation
Yes. Their peak forces can differ even though their momentum changes are equal.
Predict. Change one thing. Explain.
Compare a triangular pulse and rectangular pulse with the same peak and duration. Then reverse the peak’s sign. Predict impulse before reading the result.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Signed area = impulse = 8 N·s. Average net force=4 N over 2 s. Selected peak=8 N.
Ideal net-force pulse along one axis. Triangle starts/ends at zero; rectangle stays at the selected force. Area is signed. Shape selection changes the force history, not the mass.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a momentum or impulse relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA triangular net-force pulse starts and ends at zero, reaches +12 N and lasts 0.5 s. A 2 kg cart initially at rest receives this pulse. (a) Find impulse. (b) Find average force. (c) Find final velocity. (d) Explain why using 12 N as the average is incorrect.
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Compare with the answer and four-point rubric
- 1 point: J=½(12)(0.5)=3 N·s.
- 1 point: F_avg=3/0.5=6 N.
- 1 point: v_f=J/m=1.5 m/s in the positive direction.
- 1 point: The force is below its peak for most of the interval; a triangular pulse has half the rectangle area.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Area under F–t?
Signed impulse.
RECALL 2Height of an F–t graph?
Force at that instant.
RECALL 3Equal impulse means equal peak force?
No; shape and duration can differ.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Read impulse from a force–time graph
- J_net=signed area under F_net versus t.
- Rectangle: J=FΔt. Triangle: J=½F_peak Δt.
- F_net,avg=J_net/Δt.
Remember: Area below the time axis must subtract. Using peak force as the average overestimates a triangular pulse by a factor of two.
Conditions: Ideal net-force pulse along one axis. Triangle starts/ends at zero; rectangle stays at the selected force. Area is signed. Shape selection changes the force history, not the mass.
Refresh Kid · Unit 4 · Objectives 4.2.A, 4.2.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.2, objectives 4.2.A, 4.2.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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