FOCUSED REVIEW
Focused Review: Motion in One Dimension
Reinforce the highest-leverage algebraic kinematics skills for signs, graphs, constant acceleration, and free fall.
TIME
Approximately 15 minutes
BEST FOR
Targeted reinforcement
FINISH WITH
A readiness check
After this focused review, you'll be able to...
use the core constant-acceleration relationships, interpret motion graphs, and confirm readiness for the next study task.
Choose how you want to review
Unit Alignment
This bundle is aligned to the approved Physics Sensei unit specification. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
ARCHITECTURE: Physics Sensei Independent Mechanics
UNIT: MEC-U02 — Motion in One Dimension
SCOPE: Unit Review
PHYSICS LEVEL: Algebra-Based
BEST USED
✓ Before homework on one-dimensional kinematics
✓ Before a quiz or exam
✓ When signs, graphs, or constant-acceleration problems feel uncertain
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 15 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Recall Activity 1
Use displacement—not distance—to calculate average velocity.
A runner moves from x = 5.0 m to x = −7.0 m in 4.0 s. Find the runner’s average velocity.
Reveal Answers
−3.0 m/s.
Why it works: Δx = x_f − x_i = −7.0 − 5.0 = −12.0 m. Then v_avg = Δx/Δt = −12.0/4.0 = −3.0 m/s.
ACTIVITY 2
Recall Activity 2
Compare the change in velocity with the elapsed time and keep the sign.
A car traveling at +18 m/s brakes uniformly to +6.0 m/s in 3.0 s. Find its average acceleration.
Reveal Answers
−4.0 m/s².
Why it works: a_avg = (v_f − v_i)/Δt = (6.0 − 18)/3.0 = −4.0 m/s². The negative sign is consistent with the positive velocity decreasing.
ACTIVITY 3
Recall Activity 3
Use the signed area under a velocity–time graph to find displacement.
Velocity increases linearly from +2.0 m/s to +8.0 m/s during a 3.0 s interval. Find the displacement during the interval.
Reveal Answers
15 m.
Why it works: The signed area is a trapezoid: Δx = ½(v_i + v_f)Δt = ½(2.0 + 8.0)(3.0) = 15 m.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Reinforce the two highest-leverage relationships, then use them in representative situations.
KEY CONCEPT 1
Position, displacement, velocity, and signs
Choose a coordinate axis first. Position locates an object relative to the origin; displacement is the signed change in position. Average velocity uses displacement, not total distance. Speed is a magnitude and is never negative.
Δx = x_f − x_i; v_avg = Δx/Δt. Example: from x = +3 m to x = −9 m in 4 s, Δx = −12 m and v_avg = −3 m/s.
Sensei Note: A negative velocity means motion in the negative coordinate direction. It does not automatically mean the object is slowing down.
KEY CONCEPT 2
Constant acceleration gives a compact kinematics toolkit
When acceleration is constant, velocity changes linearly with time and position changes quadratically. Select the equation that contains the known quantities and the single unknown you need.
v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; Δx = ½(v₀ + v)t. Example: v₀ = 5 m/s, a = 2 m/s², t = 4 s gives v = 13 m/s and Δx = 36 m.
Sensei Note: These shortcut equations require constant acceleration over the interval. If the motion changes stages, reset the initial conditions for each stage.
KEY CONCEPT 3
How the Focused Ideas Connect
Signs come from the coordinate choice. Distinguish displacement from distance and velocity from speed before substituting numbers. The standard kinematics equations are powerful because acceleration is constant. Use known quantities to choose the most direct equation.
Focused strategy: Define the axis and model first, then use the relationship that directly answers the question.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Apply the reinforced ideas to two representative situations, then use the strategy card to check your setup.
PRACTICE 1
Worked Example
Separate the motion into two time intervals and carry the final velocity of the first interval into the second.
A car travels at 12.0 m/s for 5.0 s, then accelerates uniformly at 3.00 m/s² for 4.00 s. Find the total displacement and final speed.
Reveal Answers
Total displacement = 132 m; final speed = 24.0 m/s.
Why it works: First interval: Δx₁ = (12.0)(5.0) = 60.0 m. Second interval: Δx₂ = (12.0)(4.0) + ½(3.00)(4.00²) = 72.0 m. Total = 132 m. Final speed is v = 12.0 + (3.00)(4.00) = 24.0 m/s.
PRACTICE 2
Guided Problem
Use the constant-acceleration equations once with the stopping condition v = 0.
A bicycle moving at 10.0 m/s brakes with constant acceleration −2.50 m/s². Find the stopping time and stopping distance.
Reveal Answers
Stopping time = 4.00 s; stopping distance = 20.0 m.
Why it works: Use 0 = 10.0 − 2.50t to obtain t = 4.00 s. Then 0 = (10.0)² + 2(−2.50)Δx gives Δx = 20.0 m.
PRACTICE 3
Focused Setup Strategy
Before calculating, define the positive axis, list known quantities, and identify whether the motion model is qualitative, constant-acceleration, or calculus-based.
State the model and sign convention before substituting numbers.
Reveal Answers
Correct setup: axis, signs, known quantities, and model come before numerical substitution.
Why it works: This prevents sign errors and keeps the mathematical work tied to the physical motion.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Choose the equation that removes time
Identify the equation containing v, v₀, a, and Δx but not t.
An object has v₀ = 4.0 m/s, a = 3.0 m/s², and Δx = 10 m. Which constant-acceleration equation finds the final velocity without first finding time?
Reveal Answers
v² = v₀² + 2aΔx.
Why it works: It contains the desired final velocity and the given v₀, a, and Δx, but no time.
QUICK CHECK 2
Use area on a velocity–time graph
Treat the triangular region under the graph as signed displacement.
A velocity–time graph rises linearly from 0 at t = 0 to +12 m/s at t = 6.0 s. Find the displacement during the interval.
Reveal Answers
36 m.
Why it works: The displacement is the triangular area under v(t): ½(6.0 s)(12 m/s) = 36 m.
QUICK CHECK 3
Interpret Your Focused Check
Use the two results above to decide whether to continue or revisit one relationship.
Did you correctly identify the physical model and apply the matching relationship in both checks?
Reveal Answers
If yes, continue. If not, revisit only the matching concept card and try the check again.
Why it works: Focused review targets the specific relationship that needs reinforcement instead of restarting the entire unit.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Define the axis before the algebra
Signs come from the coordinate choice. Distinguish displacement from distance and velocity from speed before substituting numbers.
KEY TAKEAWAY 2
Match the equation to the model
The standard kinematics equations are powerful because acceleration is constant. Use known quantities to choose the most direct equation.
KEY TAKEAWAY 3
Use the Model Before the Numbers
Define direction, identify the motion model, and only then calculate or interpret the graph.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
Great work!
You've completed this review. Choose the next resource that best matches how confident you feel.
I'm Still Unsure
Review the key ideas and examples again.
Review Again →
I Need More Practice
Continue with additional practice for this unit.
Go to Practice →
I'm Ready
Continue to the next recommended resource.
Continue →