MathematicsChapter 5: Kinematics of Motion in a Straight Line
Distance Travelled On An Interval
Find velocity zeros, split the interval, and add absolute changes in position.
Learning objectives
- State the rule for distance travelled on an interval.
- Solve a distance travelled on an interval problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Find velocity zeros, split the interval, and add absolute changes in position.
Formula
s=t2-4t on
Where / symbols
- Distance travelled on an interval
- Find velocity zeros, split the interval, and add absolute changes in position.
CONCEPT AND RULE
Find velocity zeros, split the interval, and add absolute changes in position.
METHOD
For distance travelled on an interval, 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 s=t^2-4t on [0,4], split at t=2; total distance is 8.
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 distance travelled on an interval
- 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:
- For s=t^2-4t on [0,4], split at t=2; total distance is 8.
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
- Distance travelled on an interval
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Distance Travelled On An Interval
Sticky Notes · Formula and Worked Revision
Core Idea
- Find velocity zeros, split the interval, and add absolute changes in position.
Rule / Formula
- Find velocity zeros, split the interval, and add absolute changes in position.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For s=t^2-4t on [0,4], split at t=2; total distance is 8.
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
- Find velocity zeros, split the interval, and add absolute changes in position.
- Worked pattern: For s=t^2-4t on [0,4], split at t=2; total distance is 8.
- Final check: domain, sign, notation, units, and reasonableness.
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