FULL REVIEW
Full Review — Acceleration and Constant-Acceleration Motion — Foundational
Review the essential ideas, relationships, and problem-solving tools for Acceleration and Constant-Acceleration Motion.
TIME
45–60 minutes
BEST FOR
A complete topic review
FINISH WITH
A readiness check
After this full review, you'll be able to...
recall the essential ideas, apply them to representative problems, and determine what to study next.
Choose how you want to review
Course Alignment
This Physics Sensei Topic Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
Related Unit Review: If you need to review the complete unit material, review Motion in One Dimension here →
RESOURCE: Physics Sensei Topic Review | TOPIC ID: MEC-U03-T02 | TOPIC: Acceleration and Constant-Acceleration Motion | PARENT UNIT: MEC-U03 — Motion in One Dimension | COURSE LEVEL: Foundational
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
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 45–60 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
State the meaning in words.
What does an acceleration of −3 m/s² tell you about how velocity changes each second?
Reveal Answers
Velocity changes by −3 m/s each second.
Why it works: Acceleration is velocity change per unit time.
ACTIVITY 2
Recall Activity 2
Check the sign logic before calculating.
A cyclist has v > 0 and a < 0. Is the cyclist necessarily moving backward? Explain.
Reveal Answers
No. Positive velocity means it is still moving in the positive direction; negative acceleration means its velocity is decreasing.
Why it works: Direction of motion comes from velocity; acceleration describes how that velocity changes.
ACTIVITY 3
Recall Activity 3
Estimate the direction of change first.
A ball moving upward has positive velocity. Just before it reaches its highest point, what is the direction of its acceleration?
Reveal Answers
Downward. Gravity remains downward even while the ball is still moving upward.
Why it works: Acceleration due to gravity does not reverse at the top of the path.
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
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
Acceleration and Sign
Acceleration measures the rate at which velocity changes. Its sign indicates the direction of the velocity change, not whether an object is automatically speeding up or slowing down.
a = Δv/Δt
Example: A velocity change from +10 m/s to +4 m/s over 3 s gives a negative average acceleration.
Sensei note: Always define the positive direction before interpreting signs.
KEY CONCEPT 2
Constant Acceleration
When acceleration is constant, velocity changes by equal amounts in equal time intervals. Position does not change by equal amounts because the velocity itself is changing.
v = v₀ + at
Example: Starting from rest with a = +2 m/s² gives velocities 0, 2, 4, 6 m/s after 0, 1, 2, 3 s.
Sensei note: Constant acceleration does not mean constant velocity.
KEY CONCEPT 3
Motion Graphs under Constant Acceleration
For constant acceleration, the velocity–time graph is a straight line. The slope tells you acceleration, and the area between the velocity graph and the time axis gives displacement.
Δv = aΔt
Example: A horizontal v–t line means zero acceleration; an upward-sloping line means positive acceleration.
Sensei note: On a v–t graph, crossing v = 0 can indicate a change in direction.
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
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Worked Example
Work from the words and signs before using numbers.
A scooter moves at +4 m/s and accelerates at +1.5 m/s² for 4 s. Find its final velocity.
Reveal Answers
v = 4 + (1.5)(4) = +10 m/s.
Why it works: Constant acceleration changes velocity by aΔt.
PRACTICE 2
Guided Problem
Use the velocity relation and interpret the sign.
A car moving at +12 m/s slows with constant acceleration −3 m/s². How long does it take to reach +3 m/s?
Reveal Answers
3 = 12 − 3t, so t = 3 s.
Why it works: The negative acceleration reduces the positive velocity by 3 m/s each second.
PRACTICE 3
Independent Problem
Read the graph information as slope and signed area.
A v–t graph rises uniformly from +2 m/s at t = 0 to +8 m/s at t = 3 s. Find the acceleration and describe the motion.
Reveal Answers
a = (8 − 2)/3 = +2 m/s². Velocity stays positive and increases, so the object moves in the positive direction and speeds up.
Why it works: The graph’s constant positive slope is the acceleration, while positive velocity shows the direction of 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
Velocity Change
Calculate the acceleration.
Velocity changes from −2 m/s to −8 m/s in 3 s. What is the average acceleration?
Reveal Answers
a = [−8 − (−2)]/3 = −2 m/s².
Why it works: The velocity becomes 6 m/s more negative in 3 s.
QUICK CHECK 2
Speeding Up or Slowing Down
Decide using signs, not position.
At one instant v = +5 m/s and a = −2 m/s². Is the object speeding up or slowing down?
Reveal Answers
Slowing down.
Why it works: Velocity and acceleration have opposite signs, so speed decreases at that instant.
QUICK CHECK 3
Graph Interpretation
Use the slope of the velocity–time graph.
A straight v–t line drops from +6 m/s to 0 in 2 s. What is the acceleration?
Reveal Answers
a = (0 − 6)/2 = −3 m/s².
Why it works: The acceleration is the constant slope of the line.
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
Read the Signs
Acceleration describes the direction and rate of velocity change. Compare the signs of v and a to decide whether speed increases or decreases.
KEY TAKEAWAY 2
Constant Means Equal Velocity Changes
For constant acceleration, velocity changes linearly with time. Use a consistent sign convention from start to finish.
KEY TAKEAWAY 3
Graphs Tell the Same Story
For a velocity–time graph, slope gives acceleration and signed area gives displacement. Use graph shape and signs together.
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