**Speedy Velocity**

Isaac Newton and Velocity

Newtons laws of motion

First law: When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by a force.

Second law: The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

Second law

The first law says that an object at rest tends to stay at rest, and an object in motion tends to stay in motion, with the same direction and speed. Motion (or lack of motion) cannot change without an unbalanced force acting. If nothing is happening to you, and nothing does happen, you will never go anywhere. If you're going in a specific direction, unless something happens to you, you will always go in that direction. Forever.

The effect (acceleration) on the smaller mass will be greater (more noticeable). The effect of a large force on a baseball would be much greater than that same force acting on a truck. The difference in effect (acceleration) is entirely due to the difference in their masses.

Sir Isaac Newton was born in the county of Lincolnshire, England in 1643. His father died just months before he was born, and when he was three years old, his mother left him in the care of his grandmother. Isaac was always a top student, and went off to the University of Cambridge at age 19. While at Cambridge, Newton was influenced by the writings of Galileo, Nicholas Copernicus, and Johannes Kepler. By 1665, Newton began developing a mathematical theory that would lead to the development of calculus, one of the fundamental branches of mathematics.

F=ma

Force= the mass

of the object x the acceleration

of the object

**maths**

Some of Issac's theories

In 1670, Newton moved on to the study of optics and developed theories relating to the composition of white light and the spectrum of colours. In one of his famous experiments, he refracted white light with a prism, resolving it into its constituent colours: red, orange, yellow, green, blue, and violet. As a result of his experiments, he developed Newton’s Theory of Colour, which claimed that objects appear certain colours because they absorb and reflect different amounts of light.

In 1679, Newton continued his work on gravitation and its effects on the planets. In 1687, he published Philosophiae Naturalis Principia Mathematica (try saying that without your tongue getting tied), which contained many of his theories and his thoughts on the science and maths of velocity.

According to Newton, gravity is the reason that objects fall to the ground when dropped. Moreover, gravity is the reason why planets orbit the sun, while moons orbit planets, and why ocean tides exist. Newton’s theories remain among the most important concepts in the history of science and mathematics. There is some evidence that Newton’s ideas concerning gravity were inspired by apples falling from trees.

But the one theory that affected science and maths the most, would have to be the velocity theory, which has affected the science of rockets, bullets, engines, balls(ha ha, very funny) and countless other technologies and theories, not to mention opening up a whole new branch of mathematics.

Sir Isaac Newton

Lol, I'm so

handsome!

Sir Isaac Newton(actual)

Just ignore this

Just ignore this

The concept of velocity was a concept developed by Sir Isaac Newton. It plays a part in the gravity theory that was also made by him. One day, when an apple fell on his head(supposedly), he wondered what force made this happen, and he discovered a force which he called gravity. After finding this force, he made his laws of motion, which explain the mechanics of velocity

Sir Isaac Newton's brain

The third law says that for every action (force) there is an equal and opposite reaction(force). Forces are found in pairs. Acting forces encounter other forces in the opposite direction. There's the example of shooting a cannonball. When the cannonball is fired through the air (by the explosion), the cannon is pushed backward. The force pushing the ball out was equal to the force pushing the cannon back, but the effect on the cannon is less noticeable because it has a much larger mass.

Terminal velocity

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity acting on the object.

(for example because it was thrown downwards or it fell from a thinner part of the atmosphere or it changed shape) will slow down until it reaches terminal velocity. Drag depends on the projected area, and this is why objects with a large projected area relative to mass, such as parachutes, have a lower terminal velocity than objects with a small projected area relative to mass, such as bullets.

As the speed of an object increases, the drag force acting on the object, resultant of the substance (e.g., air or water) it is passing through, increases. At some speed, the drag or force of resistance will equal the gravitational pull on the object . At this point the object ceases to accelerate and continues falling at a constant speed called terminal velocity (also called settling velocity). An object moving downward with greater than

terminal velocity

Terminal velocity formulas

Velocity

Velocity is the rate of change of the position of an object, equal to a specification of its speed and direction of motion. Velocity gives both how fast and in what direction the object is moving. Velocity can be measured using a scalar absolute value of it called "speed". Speed can be represented by using a formula (V=d/t, check formula slide) and is represented by a rate of distance during a time interval, e.g. 15 km/hour

Velocity and

The average velocity(V{In terms of scalar absolute value, called speed}) of an object travelling a distance (D) at a constant direction and speed during a time interval-an amount of time(T) is described by the formula: V= D / T

The average velocity of an object undergoing constant acceleration is U+V/2 where U is the initial velocity and V is the final velocity.

Mathematically, terminal velocity—without considering buoyancy effects—is given by:

V= Sqr. root of 2mg/AC

V= terminal velocity

m= mass

g= acceleration due to gravity(1.0)

C= drag coefficient(which is 0.47 for a sphere)

A= The projected area of the object (for a sphere, it can be figured out using 4 pi r squared)

Velocity activity

A ball will be dropped (I wonder whose it is?) from the top of Q-blocks ramp (4.5 metres top to bottom) and the average velocity and terminal velocity will be figuired out.

Things you need: , ball (your own one please), stopwatch, tape measure, calculator (or your brain)

50m

5 seconds to fall

To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path (the object's path does not curve). Thus, a constant velocity means motion in a straight line at a constant speed.

If there is a change in speed, direction, or both, then the object is said to have a changing velocity and is undergoing an acceleration. For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.

The second law says that the acceleration of an object produced by a net (total) applied force is directly related to the magnitude of the force, the same direction as the force, and inversely related

. The second law shows that if you exert the same force on two objects of different mass, you will get different accelerations (changes in motion).

Step 2: Go to the top of the ramp balcony.

Step 3: Set the timer and measure how long it takes for the ball to drop.

Step 4: Use the calculator to figure out the average velocity and termninal velocity of the ball using the formulas on the previous slide.

P=4/3*pi r squared

Volume of a sphere (p=volume)

Step 1: Measure the Surface area and volume of the ball

"It's dinner time!"

Newton's mum yelled scribbled his notes formulae across the

Isaac Newton and the falling apple

as he furiously

full of mathematical

many pages of

his notebook

"It's getting cold!" Newton's mum

yelled,

Newton was just beginning to

this time even louder.

stand up, when a juicy red apple fell

off one of the apple

trees and nearly knocked him out "@#$% you apple!" he yelled in a very loud voice. He raged for a bit more before wondering what made that apple fall. After many experiments, hypothesising, and hard mathematical work, he came to a conclusion: a force called gravity pulled everything to the centre of an object, relative to it's mass. (After realising what started this, he must have raged at gravity)

The importance of velocity

Velocity is everywhere! Wherever there is a force on an object, velocity is there. Cars,trains, buses, US even balls have velocity. In fact, the whole universe is expanding and is being pushed by some kind of force. The WHOLE UNIVERSE has velocity. It plays a huge part in real life, and some of the greatest minds on earth have played a part in unravelling its secrets. But the truth is, we have barely scratched the surface of figuring out velocity. New formulas are being tested and made, and we are constantly finding out ways to measure and utilise velocity in real life, and we will continue to do so.

PRACTICE PROBLEMS:

1. Calculate the speed of a dog running through a field if he is covering 108 metres north-east in 54 seconds.

What is the speed of a horse in meters per second that

runs a distance of 1.2 km north in 2.4 minutes?

2.

What is the speed of a sailboat that is traveling 100 metres south-west in 120 seconds?(in metres per minute)

3.

Answers:

Q1= 2 metres per second

Q2= 0.5 km per minute

Q3= 50 metres per minute

south-west

north

north-east

NO he didn't!

dodged

The drag coefficient measures the force that pushes back when an object passes through a substance.