MathematicsChapter 5: Kinematics of Motion in a Straight Line
Acceleration As Rate of Velocity
Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
Learning objectives
- State the rule for acceleration as rate of velocity.
- Solve a acceleration as rate of velocity problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
Mathematical form
a=dv/dt
s=t3
v=3t2 and a
Where / symbols
- Acceleration as rate of velocity
- Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
CONCEPT AND RULE
Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
METHOD
For acceleration as rate of 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 s=t3, v=3t2 and a=6t.
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 acceleration as rate of velocity
- 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=t3, v=3t2 and a=6t.
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
- Acceleration as rate of velocity
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Acceleration As Rate of Velocity
Sticky Notes · Formula and Worked Revision
Core Idea
- Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
Rule / Formula
- Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For s=t3, v=3t2 and a=6t.
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
- Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.
- Worked pattern: For s=t3, v=3t2 and a=6t.
- Final check: domain, sign, notation, units, and reasonableness.
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