Easy
Momentum of a rolling ball
A bowling ball of mass 4.00 kg rolls in a straight line at 4.00 m/s. Find the magnitude of its momentum.
Hint and worked answer
Multiply mass by speed.
p = mv = (4.00 kg)(4.00 m/s)
p = 16.0 kg·m/s
A sample teaching day · No account needed
From a force to a change in motion.
Try the same sequence your students would use: a daily handout, a supported guided problem, then independent practice.
AP Physics 1 · Unit 4 · Day 1
Impulse & force–time graphs
01 · On paper
Introduce the physics.
Use the day’s handout for the warm-up, notes, and paper practice. Students can sketch, calculate, and explain their reasoning before opening the guided problem.
Open the daily handout (PDF) ↗Opens in a new tab. Teacher keys are separate and require an approved teacher account.
02 · With support
Work through Impulse Lab.
Watch the bat–ball contact, inspect the force graph, and connect its area to the ball’s change in momentum. Use the hints and worked values whenever a calculation blocks the next step.
This preview does not record classroom credit. Students doing assigned work should open Guided from their class’s lesson page.
03 · Independently
Apply the same ideas.
These fixed examples use problems from this day’s online practice. Work on paper, then open the worked answer. The full practice site generates new numbers and checks answers; these previews do not award points.
Teachers choose the daily goal and which levels to assign. Students do not have to complete every level in order.
Medium
Force over a time interval
A constant force of 100 N acts for 0.200 s. What impulse does that force deliver?
Hint and worked answer
For a constant force, the force–time area is a rectangle.
J = F Δt = (100 N)(0.200 s)
J = 20.0 N·s
N·s and kg·m/s are equivalent units of impulse.
Hard
From a changing force to speed
A 0.400 kg ball starts from rest. The net force in one direction rises linearly from zero to 200 N in 0.100 s. Find the ball’s final speed.
Hint and worked answer
The force–time area is a triangle. Its area gives the net impulse; then use Jnet = m(vf − vi).
Jnet = ½(200 N)(0.100 s) = 10.0 N·s
vf = 0 + 10.0 / 0.400
vf = 25.0 m/s
Boss
Rocket sled: connect three steps
A sled starts from rest. Its forward thrust increases linearly from 200 N to 500 N over 4.00 s. A constant 60.0 N friction force opposes its motion. A separate calibration found that a net force of 180 N produced an acceleration of 0.600 m/s². Find its speed after the thrust phase.
Hint and worked answer
Use the calibration to find the mass. Subtract the friction impulse from the thrust impulse, then find the change in speed.
m = 180 / 0.600 = 300 kg
Jthrust = ½(200 + 500)(4.00) = 1400 N·s
Jfriction = −(60.0)(4.00) = −240 N·s
Jnet = 1160 N·s
vf = 1160 / 300 = 3.87 m/s
Try generated practice next.
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