DOST-SEI Mechanical Reasoning Reviewer: Motion, Energy & Mechanical Relationships

TEACHER ABI · DOST-SEI MECHANICAL REASONING

Forces, Friction & Equilibrium

Read everyday force situations correctly: identify the forces, decide their directions, compare them, and determine whether an object stays at rest, moves at constant speed, or accelerates.

5–10 minute lesson27 original questionsMechanism-first SVG diagramsSaves progress

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Start with the five-form Skill Check.

QUICK REVIEW

Track what changes

Distance vs displacement
Distance counts the path; displacement compares final and initial position with direction.

Speed vs velocity
Velocity includes direction. Turning changes velocity even at constant speed.

Acceleration
Acceleration means velocity changes: speeding up, slowing down, or turning.

Height and energy
For the same object, greater height means greater gravitational potential energy.

Projectile motion
Gravity changes vertical motion while ideal horizontal motion continues.

Rolling
Rolling combines translation and rotation; mass distribution affects rotational inertia.

DO IT FAST

STATE → CHANGE → RESULT

STATE: identify the starting motion or energy state. CHANGE: mark exactly what changes—speed, direction, height, time, or input. RESULT: follow the physical consequence without adding an unstated assumption.

WORKED EXAMPLES

Five relationships to recognize

Turning: same speed can still mean changing velocity because direction changes.

Height: the same object has greater gravitational potential energy at the higher point.

Equal-time marks: increasing gaps mean increasing speed; equal gaps mean constant speed.

Projectile: at the highest point, vertical velocity is momentarily zero but horizontal velocity remains in the ideal model.

Rolling: equal-mass, equal-radius objects can roll differently if their mass distributions differ.

Common traps

Same speed does not mean same velocity when direction changes. Distance and displacement differ when a path reverses. A projectile is not stopped at its highest point. The heaviest rolling object does not automatically arrive first.

FIVE-FORM SKILL CHECK

Can you transfer the idea across five forms?

This diagnoses your next practice step; it does not verify mastery.

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Practice at the level you need

FRESH MASTERY CHECK

Verify the competency

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FAQ

Quick clarifications

Can acceleration happen without speeding up?
Yes. Changing direction changes velocity.

At the top of a projectile path, is it stopped?
No. Vertical velocity is momentarily zero, but horizontal velocity remains in the ideal model.

Does the heaviest rolling object always arrive first?
No. Ideal rolling can depend on rotational inertia and mass distribution.

RELATED COMPETENCIES

Continue Mechanical Reasoning

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Motion and Graphs UPCAT Reviewer: Lesson and Practice

TEACHER ABI UPCAT SCIENCE

Motion and Graphs

Translate graph shape into motion before using a formula.

5-10 minute lesson27 original questionsAdaptive practiceSaves progress

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Motion and Graph Interpretation

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QUICK REVIEW

Read the axes first: slope and area do different jobs

A position–time graph tells where an object is. Its slope is velocity. A velocity–time graph tells how velocity changes. Its slope is acceleration, while its signed area is displacement.

average speed = total distance / total timeaverage velocity = displacement / total timeacceleration = change in velocity / change in time

Position–time

Steeper slope means greater speed; horizontal means rest.

Velocity–time

Horizontal means constant velocity; area gives displacement.

DO IT FAST

Name the axes before reading the line

Problem: A position–time line rises from 0 m to 20 m in 5 s.

Recognize: The vertical axis is position, so slope means velocity.

Do it fast: (20−0)/(5−0)=4 m/s.

Why it works

The same-looking line means different things on different axes. Naming the axes prevents the most common graph error.

WORKED EXAMPLES

Five forms you should recognize

1. Position–time slope

From (2 s, 5 m) to (6 s, 17 m):

v=(17−5)/(6−2)=3 m/s

The straight line means this velocity is constant.

2. Velocity–time area

A horizontal line at 8 m/s for 5 s forms a rectangle:

displacement=(8 m/s)(5 s)=40 m

3. Negative velocity

Moving from +10 m to −2 m in 4 s:

v=[−2−10]/4=−3 m/s

The negative sign describes direction.

4. Rest versus zero position

A horizontal position–time line means the position is not changing, so velocity is zero. The line may be above or below position zero.

5. Distance versus displacement

One complete lap ends at the starting point. The path length is the lap distance, but displacement is zero because initial and final positions match.

COMMON TRAPS

Check before you commit

• Confusing graph height with slope
• Calling every rising line acceleration
• Forgetting signed area
• Mixing distance and displacement
• Ignoring units
• Treating a curved position graph as constant velocity

FIVE-FORM SKILL CHECK

Do you need the lesson-or just practice?

One original question in each form recommends your next step. It does not yet verify mastery.

CHOOSE YOUR PRACTICE

Work at the level you need.

Foundations

Build the core procedure with immediate explanations.

Core Practice

Use mixed forms with less scaffolding.

UPCAT-Style Transfer

Apply the competency in unfamiliar representations.

FRESH MASTERY CHECK

Ready to verify this competency?

A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.

QUICK ANSWERS

Motion and Graphs FAQ

Does a horizontal line always mean rest?

Only on a position–time graph. On a velocity–time graph, it means constant velocity.

Can velocity be negative?

Yes. The sign indicates direction relative to the chosen positive axis.

RELATED COMPETENCIES

Continue your science review.

MeasurementNewton’s LawsWork and Energy

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