,MECHANICS | EXAM RESCUE GUIDE
Mechanics Exam Rescue Guide
Original worked questions with recognition clues and guided practice
Use this pack to identify the physical model, translate the information into symbols and choose an
equation before calculating. It contains 18 worked questions, 12 independent practice questions and
six compact topic sections.
Independent study material with original questions. Check your current module scope and
permitted formula sheet before using it for revision.
How to use the pack
Read a representative question, cover its worked solution and choose your equations. After studying
the solution, attempt the related practice question. Use its small hint only when needed; final
answers and concise solutions are collected at the back.
Use gravitational acceleration magnitude g = 9.81 m s− 2 unless a question gives another value.
Keep extra calculator digits until the last line. Every numerical answer needs a unit and every vector
answer needs a direction or signed component.
Find a question type
Section Topic Page
01 Horizontal projectile motion 3
02 Moment of inertia by integration 5
03 Newton’s laws and force diagrams 7
04 Universal gravitation 8
05 Vertical circular motion 9
06 Elastic collisions 11
07 Motion on an incline 13
08 Hydrostatic force 15
09 Bernoulli pressure and force 17
10 Motion graphs and equations 19
11 Work and energy 21
12 Coupled masses and energy 23
13–18 Six micro sections 25
P01–P12 Practice answers and solutions 28
Mechanics practice • 2
, MECHANICS | EXAM RESCUE GUIDE
Symbols used throughout
Δ means final minus initial; subscripts i and f mean initial and final. Subscripts x and y label
coordinate components. An arrow such as ⃗ F means a vector. The symbol ∑ means add all relevant
terms. Define a positive direction before assigning signs. A negative velocity is motion opposite that
direction; speed itself is nonnegative.
The supplied sheet sometimes prints v s in its displacement equation. Here, v i explicitly means initial
velocity. The sheet also reuses letters: T may mean tension or period, P pressure or power, and W
work or weight. Each section states its own meaning.
01 Horizontal projectile motion
Original worked question
A drone moves horizontally at 2.40 m s− 1 and releases a seed capsule 1.25 m above level ground
without an extra push. How far horizontally from release does it land? Find the flight time as part of
your solution. Ignore air resistance.
Recognise the type
After release, gravity changes vertical velocity while horizontal velocity stays constant. Both
directions share the same flight time. A horizontal release means zero initial vertical velocity, not
zero total velocity. Place the origin at release; choose right and up as positive.
Translate into symbols
Given information Symbol Value and unit
Initial horizontal velocity v 𝑖𝑥 + 2.40 m s− 1
Initial vertical velocity v 𝑖𝑦 0 m s− 1
Vertical displacement Δy − 1.25 m
Acceleration components ax , a y 0, − 9.81 m s− 2
Time and horizontal displacement Δt , Δ x Unknown s; required m
Choose the equations
1 2
Δ y = v 𝑖𝑦 Δ t + ay ( Δt )
2
1 2
Δ x = v 𝑖𝑥 Δ t + ax ( Δ t )
2
Use vertical displacement first because only time is unknown there. Then use that same time
horizontally. The symbols v and a mean velocity and acceleration; the paired subscripts i x and i y
mean initial x and initial y components.
Mechanics practice • 3
Mechanics Exam Rescue Guide
Original worked questions with recognition clues and guided practice
Use this pack to identify the physical model, translate the information into symbols and choose an
equation before calculating. It contains 18 worked questions, 12 independent practice questions and
six compact topic sections.
Independent study material with original questions. Check your current module scope and
permitted formula sheet before using it for revision.
How to use the pack
Read a representative question, cover its worked solution and choose your equations. After studying
the solution, attempt the related practice question. Use its small hint only when needed; final
answers and concise solutions are collected at the back.
Use gravitational acceleration magnitude g = 9.81 m s− 2 unless a question gives another value.
Keep extra calculator digits until the last line. Every numerical answer needs a unit and every vector
answer needs a direction or signed component.
Find a question type
Section Topic Page
01 Horizontal projectile motion 3
02 Moment of inertia by integration 5
03 Newton’s laws and force diagrams 7
04 Universal gravitation 8
05 Vertical circular motion 9
06 Elastic collisions 11
07 Motion on an incline 13
08 Hydrostatic force 15
09 Bernoulli pressure and force 17
10 Motion graphs and equations 19
11 Work and energy 21
12 Coupled masses and energy 23
13–18 Six micro sections 25
P01–P12 Practice answers and solutions 28
Mechanics practice • 2
, MECHANICS | EXAM RESCUE GUIDE
Symbols used throughout
Δ means final minus initial; subscripts i and f mean initial and final. Subscripts x and y label
coordinate components. An arrow such as ⃗ F means a vector. The symbol ∑ means add all relevant
terms. Define a positive direction before assigning signs. A negative velocity is motion opposite that
direction; speed itself is nonnegative.
The supplied sheet sometimes prints v s in its displacement equation. Here, v i explicitly means initial
velocity. The sheet also reuses letters: T may mean tension or period, P pressure or power, and W
work or weight. Each section states its own meaning.
01 Horizontal projectile motion
Original worked question
A drone moves horizontally at 2.40 m s− 1 and releases a seed capsule 1.25 m above level ground
without an extra push. How far horizontally from release does it land? Find the flight time as part of
your solution. Ignore air resistance.
Recognise the type
After release, gravity changes vertical velocity while horizontal velocity stays constant. Both
directions share the same flight time. A horizontal release means zero initial vertical velocity, not
zero total velocity. Place the origin at release; choose right and up as positive.
Translate into symbols
Given information Symbol Value and unit
Initial horizontal velocity v 𝑖𝑥 + 2.40 m s− 1
Initial vertical velocity v 𝑖𝑦 0 m s− 1
Vertical displacement Δy − 1.25 m
Acceleration components ax , a y 0, − 9.81 m s− 2
Time and horizontal displacement Δt , Δ x Unknown s; required m
Choose the equations
1 2
Δ y = v 𝑖𝑦 Δ t + ay ( Δt )
2
1 2
Δ x = v 𝑖𝑥 Δ t + ax ( Δ t )
2
Use vertical displacement first because only time is unknown there. Then use that same time
horizontally. The symbols v and a mean velocity and acceleration; the paired subscripts i x and i y
mean initial x and initial y components.
Mechanics practice • 3
