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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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

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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

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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.

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