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MathidiaMathematics Academy
Year 12 synthesis
Lesson 73 of 75
Standard practice

Mechanics synthesis

Objective. Build and solve a multi-stage mechanics model.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Mechanics synthesis means building a multi-stage model that may combine kinematics, forces and Newton's laws to solve a realistic problem, such as finding when a connected system reaches a given speed. This often requires first using F=ma to find acceleration, then substituting that acceleration into SUVAT equations to find time, distance or final velocity. For example, finding acceleration from connected particles, then using v=u+at to find the time taken to reach a target speed, links two separate mechanics topics into one coherent solution.

Worked example

A system of connected particles produces an acceleration of 2m/s² from rest. As a mechanics synthesis task, find the distance travelled after 5 seconds using SUVAT.

2 … 5
Illustrated card showing 2 … 5
  1. 1Use s=ut+½at² with u=0
  2. 2Substitute a=2, t=5
  3. 3s=0+½×2×25
  4. 4s=25m

Answer: 25m

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. Students stop after finding acceleration in a mechanics synthesis problem, forgetting the question also asked for a kinematic quantity like time or distance. Always re-read the full question to check every requested quantity has been found.

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