Chapter 1 Basic Concepts & Description of motions

Basic theory summary

Measurements

The world consists of mass (m), space (l) and time (t), whose units are kg, m and s respectively in the International System (SI).

Scientific Notation

2.3 x 10^-3 =0.0023;

2.0 x 10^-3 * 5.0 x 10⁶ ;

Index and logarithmic laws

Trigonometry

SOH CAH TOH

Scalars

When we describe the state of an object, such as its mass, length and time, these quantities, we measure, completely determined by their magnitudes are called scalars.

Scalars are the quantities with no associated direction, such as mass (5 kg), length (3.4 m), time (30 s), temperature (20 °C),

Vectors

When we describe the process of an action, such as displacement, force, velocity, acceleration, these quantities, we measure, determined by both magnitude and direction are called vectors.

Vectors are the quantities defined by both magnitude and direction, such as displacement (move to right 3 m), velocity (20 m s^-1 to east), acceleration, force (20N forward), momentum, and impulse.

Geometrically, a vector that has a direction as well as a magnitude can be represented by an arrow:

• the arrow points in the direction of the action
• the length of the arrow gives the magnitude of the action in terms of a suitably chosen unit.

Vector plus

Algebraic representation of vector addition and subtraction

Vector resolutions

Fig. The vector (20 N) resolved into a horizontal component F_h and a vertical component F_v.

Sin 25 = Fv/20, Fv=20*sin25

Cos 25 = Fh/20, Fh=20*cos25

Answers

Description of Motion

Position (x) describes the location of an object at a certain point in time with respect to the origin.

• Position is a vector quantity and therefore requires a direction.

Distance (d) is the length between two positions.

• distance is a scalar quantity and therefore does a direction.

Displacement (s) the change in position of an object in a given direction.

• S = final position (x2) – initial position (x1)
• Displacement is a vector quantity and is measured in metres (m).

POSITION–TIME (x–t) GRAPHS

Speed (v) is the rate of at which the distance is travelled

• Like distance, speed is a scalar. A direction is not required when describing the speed of an object.

Velocity (v) is the rate at which displacement changes

• is a vector quantity, a direction should always be given with a velocity.

Their units are metres per second ()

VELOCITY–TIME (v–t) GRAPHS

Acceleration (a) as the rate of change of velocity

The average of acceleration is the change in velocity from the initial velocity (u) and the final velocity (v) over a period of time (t)

Acceleration is measured in metres per second per second ()

v = u + at

v² = u² +2as

Summary of formulae for kinematics

v = s/t m⋅s^-1

a = (v–u)/ Δt; m⋅s^-2;

v_avg = (v+u)/2

v = u + a t

s = ut + at²

v² = u² +2as

Projectile Motions

Galileo falling objects

A golf ball of mass 150 g is hit horizontally from the top of a 45.0 m high cliff with a speed of 25.0 m s^–1. Assuming an acceleration due to gravity of 10 m s^–2 and ignoring air resistance, calculate the:

• 1. a  time that the ball takes to land 

  2. b  distance that the ball travels from the base of the cliff 

  3. c  velocity of the ball as it lands 


d e

net force acting on the ball at points A and B acceleration of the ball at points A and B.

ACER Sample Questions

Gamsat T3 Question

GAMSAT PQ

GAMSAT PQ

GAMSAT PT

Tested topics

Estimation Question (tested in 2014UK, 2013, 2011)

“Using a few reasonable estimates, what is the rate of growth of your fingernails in m/s.”

A. 10^-3 m/s
B- 10^-6 m/s
C- 10^-9 m/s
D- 10^-12 m/s

Estimation Question (tested in 2010)

What is the rate of a guy’s hair growth if he goes to the hairdresser every six weeks and his hair has grown 1cm in that time.

A. 10^-3 m/s
B- 10^-6 m/s
C- 10^-9 m/s
D- 10^-12 m/s

2017 Projectile motion

Hammer throw – > I’ve played cricket before and watched testosterone-filled Olympians hammer-throw, so naturally I’ve mastered projectile & circular motion.

Additional Questions

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