## Course Description

### Overview

This course is targeted at Singapore Cambridge GCE O level students, but is also relevant to IGCSE students and Singapore's Integrated program students.

You've probably seen it in films or read about it in books - there's a deep shaft and our hero needs to find out how deep it is, so he (or she) takes a rock and drops it down the shaft, counting off the seconds until it hits the bottom. So if the stone takes 5 whole seconds to fall, we know that the shaft is really deep. How deep, exactly? It turns out that kinematics - the study of how objects move - provides us with a set of equations that we can use to relate the depth of the shaft to the time the stone takes to fall. This course explores all that and more in a series of short, informative videos that will broaden your knowledge of kinematics.

### Course Content

You will learn:

• How displacement, velocity and acceleration are related
• How to find the maximum speed a bus can reach on a fixed length of straight road
• How to find out how much distance a car needs to come to a halt
• The behaviour of an object in freefall
• Other cool stuff! (Some of the videos in this course are marked as "explanation videos", which go into greater depth on the topics covered. We try to bring in out-of-syllabus concepts where possible to make things more interesting and give a more complete understanding of the topic)

A link to the full O level Physics syllabus can be found here

### Course Prerequisites

You will need to know:

• How to watch videos on your computer Math Arena

The instructor is from Math Arena.The instructor is absolutely passionate about teaching and you'll find the lessons engaging and ultimately rewarding.

## Course curriculum

• 1

### Introduction

• Subject Content Requirements

• Q1 A student walks at a constant speed. He takes 100 s to walk 160 paces. The length of each pace is 0.80 m. How far does the student walk in 50s?

• 2

### Definitions

• Q2 A student measures the speed of a trolley. At one instant, the speed of the trolley is 1.0 m / s and two seconds later the speed is 4.0m/ s. What is the acceleration of the trolley?

• Q3 An object moves from P to Q in 10s with uniform acceleration. velocity at P = 5m/ s velocity at Q = 12 m/ s What is the acceleration?

• Q4 Which vehicle has an acceleration of 5 m/s2 ?

• Q5 A box is being pushed across a horizontal ground at a constant speed. If the push is stopped, the box will

• 3

### Drawing and solving with graphs

• Q6 The graph shows how the speed of a car varies with time. Which statement about the acceleration of the car between 10s and 20s is correct?

• Q7 An object travels at a constant speed of 10m/ s for 10s. During the next 5s, it accelerates uniformly to 20m/ s. What is the total distance travelled by the object?

• Q8 The speed-time graph shows the movement of a car. What does the shaded area of the graph represent?

• Q8 explanation

• Q9 The speed-time graph represents a short journey. Which distance-time graph represents the same journey?

• Q10 The graph shows how the speed of a car travelling in a straight line changes with time. Which section shows the largest acceleration?

• Q11 The speed-time graph represents the journey of a car. The dots separate different sections of the journey. There are six different sections. How many sections represent the car moving with non-uniform acceleration?

• Q12 The graph illustrates the motion of an object. Which feature of the graph represents the distance travelled by the object whilst moving at a constant speed?

• Q13 A car accelerates from traffic lights for 10 s. It stays at a steady speed for 20 s and then brakes to a stop in 3s. Which graph shows the journey?

• Q14 The graph shows the displacement-time graph of the journey of a car. What is the shape of the velocity-time graph for the journey of the car?

• Q15 The graph shows how the velocity of a racing car changes with time. Which statement describes the acceleration of the racing car for sections 1, 2 and 3?

• Q16 Determine the average velocity for the period 0 s to 80 s from the displacement-time graph.

• Q17 At which of the following times is the instantaneous velocity the greatest?

• Q18 The velocity of a car, which is decelerating uniformly, changes from 30 m/s to 15 m/s in 75m. After what further distance will it come to a rest?

• Q19 The graph shows how the velocity of a stone projected vertically upwards from the top of a cliff varies with time. The stone reaches the bottom of the cliff after 4s. How high is the cliff?

• 4

### Average speed

• Q20 A car takes 1 hour to travel 100 km along a main road and then ½ hour to travel 20 km along a side road. What is the average speed of the car for the whole journey?

• Q21 The graph below shows how the speed of a car varies of a 80s period. What is the average speed of the car?

• Q22 The speed-time graph of the motion of a bus is shown below. What is the average speed of the bus throughout the journey?

• 5

### Kinematics equations

• Q23 A bus travelling at 3 m s-1 passes a bus stop. What is the speed of the bus when it has travelled 154 m if it has been accelerating at 2 m s-2 ?

• Q23 explanation

• Q24 An aircraft moves to the start of the runway at 5.0 m s-1 and from this speed it accelerates at 8.0 m s-2 for the 10s until it takes off. What is the length of the runway?

• Q24 explanation

• Q25 A rocket starts from rest and accelerates at a uniform rate of 190 m/s2 for 2.4 seconds. What is its final velocity?

• Q25 explanation

• Q26 A car has a velocity of 15m/s. It then accelerates at a uniform rate of 3.2 m/s2 for the next 6 seconds. What distance does the car cover during this time?

• 6

### Freefall

• Q27 A skydiver falls from rest through the air and reaches terminal velocity. What is the acceleration of the skydiver during his fall?

• Q28 The speed-time graph for a falling skydiver is shown below. As he falls, the skydiver spreads out his arms and legs and then opens his parachute. Which part of the graph shows the skydiver falling with terminal velocity?

• Q29 Which graph represents the motion of a body falling vertically that reaches a terminal velocity?

• Q30 Assuming negligible air resistance, which of the following most likely shows the velocity-time graph for a bouncing ball?

• Q32 Two identical stones are dropped simultaneously from different heights. Air resistance is negligible. As the stones fall, how will the distance between them vary?

• Q31 A paper ball is released from rest and falls through the air. What will happen to the speed and acceleration of the paper ball during the first few seconds of the fall?

• 7

### Structured Questions

• SQ1 Round trip displacement

• SQ2 Road closure

• SQ3 Train acceleration distance

• SQ4 Braking distance

• SQ5 Calculate speed from skid mark length

• SQ6 Airplane runway length

• SQ7 Singaporean Tourist

• SQ8 200m dash

• SQ9 Depth of the well

• SQ10 Red traffic light braking distance

• SQ11 (part 1) Ticker-tape timer velocity and time

• SQ11 (part 2) Ticker-tape timer acceleration of freefall

• SQ12 Bank robber

• SQ13 (part 1) Toy car velocity and acceleration

• SQ13 (part 2) Toy car displacement

• SQ14 Falling diamonds

• SQ15 Dry and wet well

• SQ16 (part 1) Trampoline gymnast description of motion

• SQ16 (part 2) Trampoline gymnast height and depression of trampoline

• SQ17 Stone falling from cliff into sea

• 8

### Extra Questions Set A

• Set A Q1 What must change when a body is accelerating?

• Set A Q2 Which quantity X is calculated using this equation?

• Set A Q3 A car is brought to rest in 5 s from a speed of 10 m/s. What is the average deceleration of the car?

• Set A Q4 A tennis player hits a ball over the net. In which position is the ball accelerating?

• Set A Q5 Which speed / time graph applies to an object at rest?

• Set A Q6 Two distance/time graphs and two speed/time graphs are shown. Which graph represents an object that is at rest?

• Set A Q7 The speed-time graph shown is for a bus travelling between stops. Where on the graph is the acceleration of the bus the greatest?

• Set A Q8 The graph shows the speed of a car as it accelerates from rest. During part of this time the acceleration is uniform. What is the size of this uniform acceleration?

• Set A Q9 The diagram shows a speed-time graph for a body moving with constant acceleration. What is represented by the shaded area under the graph?

• Set A Q10 A cyclist is riding along a road when an animal runs in front of him. The graph shows the cyclist’s motion. He sees the animal at P, starts to brake at Q and stops at R. What is used to find the distance travelled after he applies the brakes?

• Set A Q11 The diagram shows the speed-time graph for an object moving at constant speed. What is the distance travelled by the object in the first 3 s?

• Set A Q12 A car accelerates from traffic lights. The graph shows how the car’s speed changes with time. How far does the car travel before it reaches a steady speed?

• Set A Q13 The graph shows the speed of a car as it moves from rest. What is the average speed of the car during the first 3 s?

• Set A Q14 Which graph shows the motion of a heavy, steel ball falling from a height of 2 m?

• Set A Q15 A stone falls freely from the top of a cliff into the sea. Air resistance may be ignored. Which graph shows how the acceleration of the stone varies with time as it falls?

• Set A Q16 A stone falls freely from the top of a cliff into the sea. Air resistance may be ignored. Which graph shows how the acceleration of the stone varies with time as it falls?

• Set A Q17 Which graph represents the motion of a body falling vertically that reaches a terminal velocity?

• Set A Q18 A free-fall parachutist falls at a constant speed. He then opens his parachute and continues to fall to Earth at a lower, constant speed. Which diagram shows how the distance fallen by the parachutist varies with time?

• 9

### Extra Questions Set B

• Set B Q1 A free-fall parachutist falls at a constant speed. He then opens his parachute and continues to fall to Earth at a lower, constant speed. Which diagram shows how the distance fallen by the parachutist varies with time?

• Set B Q2 A cart starting from rest travels a distance of 3.6 meters in 1.8 seconds. The average speed of the cart is

• Set B Q3 A car travels 20. meters east in 1.0 second. The displacement of the car at the end of this 1.0-second interval is

• Set B Q4 The average speed of a plane was 600 kilometers per hour. How long did it take the plane to travel 120 kilometers?

• Set B Q5 As a cart travels around a horizontal circular track, the cart must undergo a change in

• Set B Q6 Two cars, A and B, are 400. meters apart. Car A travels due east at 30. meters per second on a collision course with car B, which travels due west at 20. meters per second. How much time elapses before the two cars collide?

• Set B Q7 A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second interval?

• Set B Q8 One car travels 40. meters due east in 5.0 seconds, and a second car travels 64 meters due west in 8.0 seconds. During their periods of travel, the cars definitely had the same

• Set B Q9 In a 4.0-kilometer race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6.0 minutes. The average speed of the runner for the race is

• Set B Q10 A jogger accelerates at a constant rate as she travels 5 meters along a straight track from point A to point B. If her speed was 2 m/s at point A and will be 3 m/s at point B, how long will it take her to go from A to B?

• Set B Q11 A 1000-kilogram car traveling with a velocity of +20. meters per second decelerates uniformly at –5.0 meters per second^2 until it comes to rest. What is the total distance the car travels as it decelerates to rest?

• Set B Q12 A car is accelerated at 4.0 m/s2 from rest. The car will reach a speed of 28 meters per second at the end of

• Set B Q13 A car is accelerated at 4.0 m/s2 from rest. The car will reach a speed of 28 meters per second at the end of

• Set B Q14 An object has a constant acceleration of 2.0 m s-2 . The time required for the object to accelerate from 8.0 meters per second to 28 meters per second is

• Set B Q15 A bicyclist accelerates from rest to a speed of 5 m/s in 10 seconds. During the same 10 seconds, a car accelerates from a speed of 22 m/s to a speed of 27 m/s. Compared to the acceleration of the bicycle, the acceleration of the car is

• Set B Q16 A car having an initial velocity of 12 meters per second east slows uniformly to 2 meters per second east in 4.0 seconds. The acceleration of the car during this 4.0-second interval is

• Set B Q17 A ball dropped from rest falls freely until it hits the ground with a speed of 20 meters per second. The time during which the ball is in free fall is approximately

• Set B Q18 An observer recorded the data above for the motion of a car undergoing constant acceleration. What was the magnitude of the acceleration of the car?

• Set B Q19 If the mass of an object were doubled, its acceleration due to gravity would be

• Set B Q20 As an object falls freely near the surface of the Earth, its velocity

• Set B Q21 As a body falls freely near the surface of the Earth, its acceleration

• Set B Q22 Base your answers to the following two questions on the graphs below. The graphs represent various phenomena in physics.

• Set B Q23 Which graph best represents the motion of a freely falling body near the Earth's surface?

• Set B Q24 As shown in the diagram below, an astronaut on the Moon is holding a baseball and a balloon. The astronaut releases both objects at the same time. What does the astronaut observe?

• Set B Q25 Objects A and B are dropped from rest near Earth’s surface. Object A has mass m and object B has mass 2m. What are the speed and distance of fall of object B after 2 seconds of free fall?

• Set B Q26 A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock’s speed to the stone’s speed is

• Set B Q27 Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls?

• Set B Q28 A stone is dropped from a bridge 45 meters above the surface of a river. Approximately how many seconds does the stone take to reach the water's surface?

• Set B Q29 A ball is thrown straight up with a speed of 12 meters per second near the surface of Earth. What is the maximum height reached by the ball?

• Set B Q30 The graph at the right represents the relationship between distance and time for an object in motion. During which interval is the speed of the object changing?

• Set B Q31 The graph below represents the relationship between distance and time for an object. What is the instantaneous speed of the object at t = 5.0 seconds?

• Set B Q32 The displacement-time graph below represents the motion of a cart along a straight line. During which interval was the cart accelerating?

• Set B Q33 The graph at the right represents the relationship between distance and time for an object moving in a straight line. According to the graph, the object is

• Set B Q34 The graph at the right represents the motion of a body that is moving with

• Set B Q35 The graph below represents the displacement of an object as a function of time.

• Set B Q36 Which two graphs best represent the motion of an object falling freely from rest near Earth's surface?

• Set B Q37 The diagram below shows a 1-kilogram stone being dropped from a bridge 100 meters above a gorge. Which graph of distance traveled versus time represents the motion of the freely falling stone?

• Set B Q38 Which pair of graphs represents the same motion of an object?

• Set B Q39 The graph at the below shows the relationship between speed and time for two objects, A and B. Compared with the acceleration of object B, the acceleration of object A is

• Set B Q40 The diagram below represents the relationship between velocity and time of travel for four cars, A, B, C, and D, in straight-line motion. Which car has the greatest acceleration during the time interval 10. seconds to 15 seconds?

• Set B Q41 Base your answers to the next 3 questions on the graph below which represents the relationship between velocity and time for a 2.0-kilogram cart that is initially at rest and starts moving northward.

• Set B Q42 The speed-time graph shown on the below represents the motion of an object. Which graph best represents the relationship between acceleration and time for this object?

• 10

### Extra Questions Set C

• Set C Q1 A boy takes 5s to walk from point P to point Q, and takes 5s to walk from point Q to point R, and then takes another 5s to walk from point R to point S. PQRS is a square with side 10m. Find his average speed and velocity from P to S.

• Set C Q2 A toy car is traveling at a constant speed to the left. Balls are projected vertically upward from the toy at one-second intervals. Which diagram best shows a possible snapshot of the car and the balls after the third ball has been projected?

• Set C Q3 A ball of mass 0.40 kg approaches a soccer player with a speed of 10 m s-1 .The player kicks the ball back in the opposite direction with a speed of 20 m s-1 .The time of contact is 0.10s. What is the force exerted on the ball?

• Set C Q4 A body X of mass m is dropped from a height h. At the same time, another body Y of mass 3m is dropped from a height 3h. Which of the following statement is true?

• Set C Q5 A stone is thrown downward with a speed of 18 m s-1. Just before hitting the ground, it has a final speed of 42 m s-1 . If the stone was thrown horizontally with the same speed, what speed would it have before hitting the ground?

• Set C Q6 A rescue plane is flying horizontally with a speed of 30 ms-1 and at an altitude of 125 m above the sea when it drops a warning flare. How far from the plane is the flare when it hits the water?

• Set C Q7 Persons A and B walk at an average speed of 0.90 m s-1 and 0.80 m s-1 respectively. Person B walks on a travelator but person A does not. The travelator moves at the speed of 0.50 m s-1 .How much faster will person B take to travel 50m?

• Set C Q8 A ball thrown up reaches a height of 0.50 m. How high up will the same ball reach if it is being thrown up with twice the initial speed?

• Set C Q9 The diagram below shows a velocity-time graph for a motor car. What is the average speed in m s-1 of the car in the first 5 seconds?

• Set C Q10 A bullet is fired towards a nearby tree with a speed of 200 m s-1. The bullet is later found at a depth of 5.0 cm. Find the average deceleration of the bullet inside the tree.

• Set C Q11 A girl throws a ball vertically with a velocity of 2.0 m s-1 .What 5 the time taken for the ball to fall back to her hand?

• Set C Q12 The hammer of a pile driver hits a steel girder with a speed of 6 m s-1. If it drives the girder 10 cm into the ground, what is the average deceleration of the hammer?

• Set C Q13 A car moving at constant speed of 20 m s-1 suddenly decelerates uniformly at 2.0 m s-2. What is the distance traveled by the car during the second just before it stops?

• Set C Q14 A girl throws a ball vertically upwards with a speed of 10 m s-1 . What is the acceleration of the ball one second after leaving the girl's hand?

• Set C Q15 The diagram below shows a series of photographs of a ball rolling with constant velocity. The camera was taking pictures at a constant rate of 20 per second. What was the speed of the ball?

• Set C Q16 A basketball is thrown vertically downwards with a speed of 10 m s-1 at a height of 8 m from the ground and bounces. Which of the following graphs correctly represent the relation between the speed and time of the ball?

• Set C Q17 A small block of metal slides along a horizontal frictionless surface collides against the wall and rebounds along its original path. Which of the following graphs represent the variation of velocity v with time t?

• Set C Q18 A small ball is given an initial push up an inclined slope. It moves up the frictionless slope and down again. Which of the following graphs best represents the velocity-time graph of its motion from point A to B and back to A again?

• Set C Q19 A stone rolls off the edge of a vertical cliff. Neglecting air resistance, which of the following best describes its subsequent motion?

• Set C Q20 Velocity-time graph, deceleration and distance travelled for a cyclist

• Set C Q21 Velocity-time graph, acceleration, distance travelled and average velocity of a locomotive

• Set C Q22 Distance, average speed and type of motion for a bus