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Greatest and Least Velocity
Extrema of velocity occur where a=v'=0 or at interval endpoints.
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Greatest and Least Velocity
What is it?
Extrema of velocity occur where a=v'=0 or at interval endpoints.
In simple words
- Extrema of velocity occur where a=v'=0 or at interval endpoints.
- Worked pattern: For v=t^2-4t+5, a=2t-4=0 at t=2, giving minimum v=1.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Greatest and least velocity: Extrema of velocity occur where a=v'=0 or at interval endpoints.
What you should learn
- State the rule for greatest and least velocity.
- Solve a greatest and least velocity problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Extrema of velocity occur where a=v'=0 or at interval endpoints.
CONCEPT AND RULE
Extrema of velocity occur where a=v'=0 or at interval endpoints.
METHOD
For greatest and least velocity, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For v=t2-4t+5, a=2t-4=0 at t=2, giving minimum v=1.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve greatest and least velocity
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Greatest and least velocity
- rule
- worked example
- worked example
How the ideas connect
Worked example: For v=t^2-4t+5, a=2t-4=0 at t=2, giving minimum v=1.
Deeper understanding
Go beyond memorising Greatest and Least Velocity. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: For v=t^2-4t+5, a=2t-4=0 at t=2, giving minimum v=1.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Greatest and least velocity
- rule
- worked example
- Greatest and least velocity: Extrema of velocity occur where a=v'=0 or at interval endpoints.
- CONCEPT AND RULE: Extrema of velocity occur where a=v'=0 or at interval endpoints.
- METHOD: For greatest and least velocity, identify the given information and required result. Select the matc
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Greatest and Least Velocity: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Greatest and least velocity
- rule
- worked example
- Greatest and least velocity: Extrema of velocity occur where a=v'=0 or at interval endpoints.
Important formulas
- Greatest and least velocity
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Greatest and least velocity
rule
worked example
Greatest and least velocity: Extrema of velocity occur where a=v'=0 or at interval endpoints.
Extrema of velocity occur where a=v'=0 or at interval endpoints.
- Definition
- Extrema of velocity occur where a=v'=0 or at interval endpoints.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Greatest and Least Velocity.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Greatest and Least Velocity and say why it fits.
Mistake
Q4. State one common mistake students make about Greatest and Least Velocity.
Exam note
Q5. Write a short exam note on Greatest and Least Velocity: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.