MathematicsChapter 5: Kinematics of Motion in a Straight Line
Speeding Up and Slowing Down
Motion speeds up when v and a have the same sign and slows when their signs differ.
Learning objectives
- State the rule for speeding up and slowing down.
- Solve a speeding up and slowing down problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Motion speeds up when v and a have the same sign and slows when their signs differ.
Where / symbols
- Speeding up and slowing down
- Motion speeds up when v and a have the same sign and slows when their signs differ.
CONCEPT AND RULE
Motion speeds up when v and a have the same sign and slows when their signs differ.
METHOD
For speeding up and slowing down, 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 v<0 and a<0, speed increases.
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 speeding up and slowing down
- 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 v<0 and a<0, speed increases.
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
- Speeding up and slowing down
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Speeding Up and Slowing Down
Sticky Notes · Formula and Worked Revision
Core Idea
- Motion speeds up when v and a have the same sign and slows when their signs differ.
Rule / Formula
- Motion speeds up when v and a have the same sign and slows when their signs differ.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- If v<0 and a<0, speed increases.
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
- Motion speeds up when v and a have the same sign and slows when their signs differ.
- Worked pattern: If v<0 and a<0, speed increases.
- Final check: domain, sign, notation, units, and reasonableness.
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