Senior Three Physics Notes by Anonymous

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Chapter 1

Kinematics: Motion Graphs and Equations

Key Concepts

This chapter covers how to read displacement-time and velocity-time graphs, and how to use SUVAT equations to solve motion problems. For exams, you must convert what the graph “says” (area/slope) into the correct variables (s, u, v, a, t).

Core ideas you MUST know:

• Displacement-time (s-t) graphs

• Gradient (slope) = velocity (constant gradient → constant velocity)

• Area under the graph = not used for s-t unless you have a v-t graph; for s-t, read displacement directly at times

• Velocity-time (v-t) graphs

• Gradient (slope) = acceleration

• Area under v-t graph = displacement

• Constant acceleration patterns

• v-t graph is a straight line when acceleration is constant

• s-t graph is a curve (parabola) when acceleration is constant (because velocity changes)

• SUVAT equations (constant acceleration)

• Use only if acceleration is constant and motion is straight-line

• Choose the equation that matches the given variables (avoid mixing cases)

• Sign convention

• Decide positive direction; velocities/displacements opposite direction become negative

Before you continue:

If a v-t graph is a horizontal line at +3 m/s for 5 s, what are the acceleration and displacement?

Key Terms

Displacement - change in position (can be negative depending on chosen direction).

Velocity - rate of change of displacement; includes direction (m/s).

Acceleration - rate of change of velocity; can be positive or negative (m/s^2).

Displacement-time graph (s-t) - graph of displacement vs time.

Velocity-time graph (v-t) - graph of velocity vs time.

Gradient (slope) - change in y divided by change in x on a graph.

Area under a v-t graph - equals displacement during that time interval.

Active Recall

Displacement - __________________________________________________

__________________________________________________

Velocity - __________________________________________________

__________________________________________________

Acceleration - __________________________________________________

__________________________________________________

Displacement-time graph (s-t) - __________________________________________________

__________________________________________________

Velocity-time graph (v-t) - __________________________________________________

__________________________________________________

Gradient (slope) - __________________________________________________

__________________________________________________

Area under a v-t graph - __________________________________________________

__________________________________________________

Worked Examples

Example 1: Read acceleration from a v-t graph (straight line)

A car moves with velocity increasing from 2 m/s to 10 m/s in 4 s. Find the acceleration.

• Use acceleration = gradient of v-t graph = (final v - initial u) / t

• a = (10 - 2) / 4 = 8 / 4 = 2 m/s^2

• Acceleration is positive because velocity increases in the positive direction.

Now you try

A runner’s velocity increases from 6 m/s to 18 m/s in 3 s. Find the acceleration.

__________________________________________________

Example 2: Displacement from area under a v-t graph

A bus slows from 20 m/s to 10 m/s uniformly over 5 s. Find the displacement.

• For constant acceleration, v-t graph is a trapezium.

• Displacement = area = (1/2) x (sum of parallel sides) x height

• Parallel sides are 20 and 10; height is 5 s

• s = (1/2) x (20 + 10) x 5 = (1/2) x 30 x 5 = 75 m

Now you try

A bicycle speeds up uniformly from 4 m/s to 14 m/s in 6 s. Find the displacement.

__________________________________________________

Example 3: SUVAT equation selection

A train accelerates from rest (u = 0) to 25 m/s in 5 s with constant acceleration. Find acceleration and distance.

• Known: u = 0, v = 25, t = 5

• a = (v - u) / t = (25 - 0) / 5 = 5 m/s^2

• Use s = (u + v)/2 x t for constant acceleration

• s = (0 + 25)/2 x 5 = 12.5 x 5 = 62.5 m

Now you try

A scooter starts at 3 m/s and reaches 15 m/s after 4 s (constant acceleration). Find distance travelled.

__________________________________________________

Practice Questions

• (Easy) A displacement-time graph is a straight line increasing. State what this tells you about the acceleration.

__________________________________________________

• (Easy) A v-t graph is a horizontal line at -2 m/s for 8 s. Find the displacement in 1 sentence.

__________________________________________________

• (Medium) A particle has velocity decreasing from 12 m/s to 6 m/s over 3 s uniformly. Calculate its acceleration.

__________________________________________________

• (Medium) A vehicle has v = 5 m/s at t = 0 and v = 17 m/s at t = 4 s with constant acceleration. Calculate the displacement from t = 0 to t = 4 s.

__________________________________________________

• (Hard) A displacement-time graph shows s increases from 0 m to 60 m in 6 s with constant speed. Calculate the velocity and state the type of v-t graph you expect.

__________________________________________________

• (Hard) A runner moves in the positive direction. From t = 0 to 5 s, v increases uniformly from 2 m/s to 10 m/s. From t = 5 s to 9 s, v is constant at 10 m/s. Calculate the total displacement from t = 0 to 9 s.

__________________________________________________

Answer Key

• Acceleration = 0 (constant speed).

• Displacement = v x t = -2 x 8 = -16 m.

• a = (v - u)/t = (6 - 12)/3 = -2 m/s^2.

• Use average velocity: s = (u + v)/2 x t = (5 + 17)/2 x 4 = 44 m.

• v = s/t = 60/6 = 10 m/s; v-t is a horizontal line at +10 m/s.

• From 0-5 s: s1 = (u+v)/2 x t = (2+10)/2 x 5 = 30 m. From 5-9 s: s2 = v x t = 10 x 4 = 40 m. Total = 70 m.

Exam Tips & Common Mistakes

• Confusing displacement with distance: displacement includes direction (negative possible), distance is always positive.

• Reading “slope” the wrong way: on an s-t graph, slope gives velocity; on a v-t graph, slope gives acceleration.

• Using SUVAT when acceleration is not constant: if the graph is curved, don’t assume constant acceleration.

• Forgetting signs: a negative velocity means motion in the negative direction, not “less speed”.

• Mixing up u, v, and t: always write the given values clearly with units before choosing an equation.

Quick Reference

Main rules (SUVAT + graphs)

• Constant acceleration: v = u + a t

• Constant acceleration: s = u t + 1/2 a t^2

• Constant acceleration: v^2 = u^2 + 2 a s

• Constant acceleration (average velocity): s = (u + v)/2 x t

• Graph links:

• s-t slope = velocity

• v-t slope = acceleration

• area under v-t = displacement (with sign)

Mnemonic

• “S-V-A-T” equations:

• v = u + a t

End of chapter one. 4 more chapters in the full book.

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What's inside: 5 chapters

1. Kinematics: Motion Graphs and Equations
2. Forces and Newton’s Laws in Practice
3. Work, Energy, and Power Calculations
4. Momentum, Impulse, and Collisions
5. Electric Circuits: EMF, Internal Resistance

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"Senior Three Physics Notes" is a study guide book by Anonymous with 5 chapters and approximately 5,198 words. Senior Three physics study notes aligned to a new curriculum.

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