MathematicsChapter 5: Kinematics of Motion in a Straight Line
Velocity As Rate of Position
Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
Learning objectives
- State the rule for velocity as rate of position.
- Solve a velocity as rate of position problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
Mathematical form
v=ds/dt
s=t2-4t
v=2t-4.
Where / symbols
- Velocity as rate of position
- Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
CONCEPT AND RULE
Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
METHOD
For velocity as rate of position, 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
If s=t2-4t, v=2t-4.
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 velocity as rate of position
- 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.
Worked example
- Worked example:
- If s=t2-4t, v=2t-4.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Velocity as rate of position
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Velocity As Rate of Position
Sticky Notes · Formula and Worked Revision
Core Idea
- Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
Rule / Formula
- Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- If s=t2-4t, v=2t-4.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Instantaneous velocity is v=ds/dt; its sign gives direction along the chosen axis.
- Worked pattern: If s=t2-4t, v=2t-4.
- Final check: domain, sign, notation, units, and reasonableness.
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