MathematicsChapter 5: Kinematics of Motion in a Straight Line
Rest and Change of Direction
A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
Learning objectives
- State the rule for rest and change of direction.
- Solve a rest and change of direction problem step by step.
- Check the result, restrictions, notation, and units.
Definition
A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
Mathematical form
v=t-2 changes from negative to positive at t=2.
v=t-2 changes from negative to positive at
t=2.
Where / symbols
- Rest and change of direction
- A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
CONCEPT AND RULE
A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
METHOD
For rest and change of direction, 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
v=t-2 changes from negative to positive at t=2.
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 rest and change of direction
- 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:
- v=t-2 changes from negative to positive at t=2.
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
- Rest and change of direction
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Rest and Change of Direction
Sticky Notes · Formula and Worked Revision
Core Idea
- A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
Rule / Formula
- A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- v=t-2 changes from negative to positive at t=2.
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
- A particle is instantaneously at rest when v=0; direction changes only if velocity changes sign.
- Worked pattern: v=t-2 changes from negative to positive at t=2.
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.