Ch 2 · 1.2 Motion · O Level Physics 5054

Topic 2 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 78 lessons.

Introduction

How fast is a car going, and is it speeding up? Motion is described with three ideas, speed, velocity and acceleration, and two kinds of graph. Motion graphs appear in almost every O Level paper, so reading their shapes, gradients and areas quickly is worth a lot of marks. (Syllabus section 1.2.)

Key ideas — Speed and velocity

Speed is the distance travelled per unit time. Velocity is the change in displacement per unit time, so it has a direction: velocity is a vector, speed is a scalar.

🧑‍🏫 Teacher's explanation

Imagine you are walking to a friend's house. If you walk 100 meters in 50 seconds, your speed is 2 m/s. This tells you how fast you are moving, but it doesn't tell you where you ended up. If you walk 50 meters forward and then 50 meters back to your starting point, your total distance is 100 meters, but your total displacement is 0 meters. This is why velocity is different from speed; velocity cares about the direction and the change in position from start to finish.

📖 Definitions

🔍 Worked example — Easy

A cyclist travels 1200 m in 60 s. Calculate the average speed.

🔍 Worked example — Standard

A car accelerates from 5 m/s to 25 m/s in 4 s. Calculate the acceleration.

🔍 Worked example — Exam-style

A train starts from rest and accelerates uniformly to a speed of 30 m/s over a distance of 500 m. Calculate the time taken.

⚠️ Common errors

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🎯 Exam question

Key ideas — Acceleration

Acceleration is the change in velocity per unit time:

🧑‍🏫 Teacher's explanation

Imagine you are driving a car. If you press the accelerator, your speedometer needle moves up; this change in speed is acceleration. If you press the brake, the needle moves down; this is deceleration. Acceleration isn't just about how fast you are going, but how quickly your speed is changing.

📖 Definitions

🔍 Worked example — Easy

A cyclist increases their velocity from 3 m/s to 9 m/s in 3 s. Calculate the acceleration.

🔍 Worked example — Standard

A car traveling at 25 m/s comes to a complete stop in 5 s. Calculate the deceleration.

🔍 Worked example — Exam-style

A stone is dropped from a cliff. It accelerates at g = 9.8 m/s^2. Calculate the distance travelled by the stone after 4.0 s (assume it starts from rest).

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Uniform and non-uniform acceleration

(e.g. a ball rolling down a straight ramp, an object falling freely with no air resistance).

🧑‍🏫 Teacher's explanation

Imagine you are driving a car. If you press the accelerator pedal and hold it in a fixed position, your speedometer might increase by exactly 5 km/h every single second. This steady, predictable increase is called uniform acceleration. It is like climbing a staircase where every step is exactly the same height.

📖 Definitions

🔍 Worked example — Easy

A cyclist starts from rest and reaches a velocity of 8 m/s in 4 s. Calculate the acceleration.

🔍 Worked example — Standard

A car traveling at 25 m/s brakes to a stop in 5 s. Calculate the deceleration.

🔍 Worked example — Exam-style

A ball is dropped from a height. It accelerates at 9.8 m/s^2 for 3.0 s. Calculate the total distance traveled.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Deceleration

A deceleration is a negative acceleration: the velocity is decreasing. A car slowing from 20 m/s to 8 m/s in 4.0 s has a = 8 - 20/4.0 = -3.0\ m/s^2, a deceleration of 3.0\ m/s^2.

🧑‍🏫 Teacher's explanation

Imagine you are riding a bicycle and you see a red light ahead. To stop, you squeeze the brakes. As you squeeze, your speed drops from a fast pace to a slow crawl, and eventually to zero. This process of losing speed is what we call deceleration. In physics, we don't like having two different words for 'changing speed' if we can help it, so we treat deceleration simply as 'negative acceleration'.

📖 Definitions

🔍 Worked example — Easy

A cyclist is traveling at 12 m/s. They apply the brakes and come to a complete stop in 6.0 s. Calculate the deceleration.

🔍 Worked example — Standard

A car accelerates from 5.0 m/s to 25 m/s in 5.0 s. Calculate the acceleration.

🔍 Worked example — Exam-style

A train decelerates uniformly from 30 m/s to 10 m/s over a distance of 100 m. Calculate the time taken for this deceleration.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Free fall

Near the Earth's surface, the acceleration of free fall, g, is approximately constant and approximately 9.8\ m/s^2, for every object, provided air resistance can be ignored.

🧑‍🏫 Teacher's explanation

Imagine you drop a tennis ball from a tall building. As it falls, it doesn't just move at a steady pace; it gets faster and faster every single second. This 'increase in speed' is what we call acceleration. In a vacuum (where there is no air to push back against the ball), gravity pulls on everything with the exact same strength.

📖 Definitions

🔍 Worked example — Easy

A stone is dropped from the top of a cliff. Calculate its velocity after 3.0 s of free fall. Assume g = 10 m/s^2 and ignore air resistance.

🔍 Worked example — Standard

An object falls from rest with an acceleration of g = 9.81 m/s^2. Calculate the total distance travelled after 4.0 s.

🔍 Worked example — Exam-style

A skydiver is falling towards Earth. Their velocity increases from 15 m/s to 45 m/s in 3.0 s. Calculate the acceleration of the skydiver. (Note: This is not free fall due to air resistance, but tests the acceleration formula).

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Distance–time graphs

Read the shape:

🧑‍🏫 Teacher's explanation

Imagine you are tracking a friend's journey using a GPS that only records their position at specific times. A distance-time graph is just a visual way to tell their story. If the line is flat, they've stopped for a snack. If the line is a straight diagonal, they are walking at a steady pace. If the line starts flat and then curves upwards like a ramp, they are speeding up (accelerating).

📖 Definitions

🔍 Worked example — Easy

A car travels 50 m in 10 s along a straight road. Calculate the speed from the distance-time graph gradient.

🔍 Worked example — Standard

A runner's position is plotted on a distance-time graph. The line is a straight diagonal from (0, 0) to (20 s, 100 m). Calculate the speed.

🔍 Worked example — Exam-style

A cyclist moves such that their distance s follows the equation s = 2t^2 (where s is in meters and t is in seconds). Determine the speed at t = 3 s by calculating the gradient of the curve.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

(a) Calculate the speed of the car between t = 0 s and t = 4 s. (b) Describe the motion of the car between t = 4 s and t = 10 s. [3 marks]

Key ideas — Speed–time graphs

🧑‍🏫 Teacher's explanation

Imagine you are watching a car's speedometer. A speed-time graph is just a visual diary of what that speedometer is doing over time. If the needle stays stuck on 50 km/h, the graph is a flat horizontal line. If the needle is moving steadily upwards, the car is speeding up at a constant rate.

📖 Definitions

🔍 Worked example — Easy

A cyclist starts from rest and reaches a speed of 12 m/s in 6 s with constant acceleration. Calculate the acceleration.

🔍 Worked example — Exam-style

A ball is dropped from a height. It accelerates from 0 m/s to 29.4 m/s in 3 s. Sketch the speed-time graph characteristics and calculate the distance fallen during this time.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Worked example

Example 1: average speed. A bus travels 6.0 km in 10 minutes, waits 5 minutes, then travels 3.0 km in 5 minutes. Find its average speed in m/s.

🔍 Worked example — Easy

A cyclist travels 4.5 km in 15 minutes. Calculate the average speed in m/s.

🔍 Worked example — Standard

A car accelerates from 5.0 m/s to 25 m/s in 5.0 s. Calculate the acceleration.

🔍 Worked example — Exam-style

A speed-time graph shows an object starting from rest (0 m/s), accelerating uniformly to 12 m/s in 4.0 s, moving at this constant speed for 6.0 s, and then decelerating uniformly to rest in 2.0 s. Calculate the total distance travelled.

⚠️ Common errors

Common mistakes

Practice

Answers: (1) 1800 ÷ 240 = 7.5\ m/s. (2) a = (27 - 12)/5.0 = 3.0\ m/s^2. (3) a = (10 - 30)/25 = -0.80\ m/s^2; the negative sign means the train is decelerating. (4) (a) at rest, (b) constant acceleration, (c) acceleration decreasing (non-uniform acceleration). (5) tfrac12 × 4.0 × 8.0 + 8.0 × 6.0 = 16 + 48 = 64\ m. (6) Uniform: velocity changes by the same amount each second (e.g. free fall without air resistance). Non-uniform: the change per second varies (e.g. a car in traffic).

Ch 2 · 1.2 Motion · O Level Physics 5054

All chapters in Motion, Forces and Energy