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IB Guides

2.1.1 Define displacement, velocity, speed and acceleration.

Displacement
Displacement is the distance moved in a particular direction. It is a vector quantity.

SI unit: m
Symbol: s

Velocity
Velocity is the rate of change of displacement. It is a vector quantity.
Velocity = (change in displacement / change in time)

SI unit: m s-1
Symbol: v or u

Speed
Speed is the rate of change of distance. It is a scalar quantity.
Speed = (change in distance / change in time)

SI unit: m s-1
Symbol: v or u

Note that speed and velocity are not the same thing. Velocity has a direction.

Acceleration
Acceleration is the rate of change of velocity. It is a vector quantity.
Acceleration = (change in velocity / change in time)

SI unit: m s-2
Symbol: a

Note that acceleration is any change in velocity, meaning an increase or decrease in velocity or a change in direction.

2.1.2 Explain the difference between instantaneous and average values of speed, velocity and acceleration.

Instantaneous
An instantaneous value of speed, velocity or acceleration is one that is at a particular point in time.

Average
An average value of speed, velocity or acceleration is one that is taken over a period of time.

2.1.3 Outline the conditions under which the equations for uniformly accelerated motion may be applied.

The equations of uniformly accelerated motion can only be under conditions where the acceleration is constant.

The equations of uniformly accelerated motion are as follows:

Table 1.2.1 - Variables used in uniformly accelerated motion equations

Other equations may be derived from these equations.

2.1.4 Identify the acceleration of a body falling in a vacuum near the Earth?s surface with the acceleration g of free fall.

When we ignore the effect of air resistance on an object falling down to earth due to gravity we say the object is in free fall. Free fall is an example of uniformly accelerated motion as the only force acting on the object is that of gravity.

On the earths surface, the acceleration of an object in free fall is about 9.81 ms-1. We can easily recognise the uniform acceleration in displacement - time, velocity - time and acceleration - time graphs as shown below:

2.1.5 Solve problems involving the equations of uniformly accelerated motion.

A car accelerates with uniformly from rest. After 10s it has travelled 200 m.

Calculate:

Its average acceleration

S = ut + 1/2 at²

200 = 0 x 10 +  1/2  x a x 10²

200 = 50a

a = 4 m s-2

Its instantaneous speed after 10s

v² = u ² + 2as

= 0 + 2 x 4 x 10

= 80

V= 8.9 m s-1

2.1.6 Describe the effects of air resistance on falling objects.

Air resistance eventually affects all objects that are in motion. Due to the effect of air resistance objects can reach terminal velocity. This is a point by which the velocity remains constant and acceleration is zero.

In the absence of air resistance all objects have the same acceleration irrespective of its mass.

2.1.7 Draw and analyse distance?time graphs, displacement?time graphs, velocity?time graphs and acceleration?time graphs.

2.1.8 Calculate and interpret the gradients of displacement?time graphs and velocity?time graphs, and the areas under velocity?time graphs and acceleration?time graphs.

Determining its velocity
We know that the gradient of a displacement – time graph gives us its velocity. Therefore for the first 5 seconds the speed is:

25/5 =5ms?¹

After the first 5 s the object is stationary for 3 s. For these 3s its velocity is zero.

After 8s the object starts to return at a faster speed then before. From the graph we find the speed to be:

25/2 =12.5ms?¹

Figure 2.1.5 – Velocity -Time graph 

Determine its acceleration
We know that the gradient of a velocity- Time graph gives us its acceleration. Therefore for the first 5 s the acceleration is:

50/5 =10 ms?²

When the object is at constant speed from 5s to 7s its acceleration is zero. During the last second of the objects journey the object is decelerating at:

50/1 =50 ms?² 

Determine its displacement
The area under a velocity-time graph is the displacement. During the first 5 s the object has travelled:

 ½ x 5 x 50 = 125m

Determine the change in velocity
The area under the acceleration- Time graph gives us the change in velocity

From the graph we find that the change in velocity is 10 x 3 = 30 ms?¹

Note: The gradient of the acceleration - time graph is actually the rate of change of acceleration. However it isn’t often useful.

2.1.9 Determine relative velocity in one and in two dimensions.

MIT 6.0001 Notes

Journal - 6 Oct 2020

Introduction to Computational Thinking and Data Science

Lecture 1 

1. Computational models: optimisation, simulation, statistical

2. Lambda function

3. Optimisation model: optimise with constraints 

    a. Brute force algorithm

    b. Greedy algorithm (doesn't always yield the best result)

Lecture 2 

Brute force algorithm

1. Left-most and depth-most enumeration

Paused at 13:00

Startup Lessons

Lecture 1.

• Be real builders. Real recognise real. 
• Too much money, plenty of good people, and plenty of good problems to solve. 

Lecture 2.

• Show, don't tell
• Don't use buzzwords
• Write using journalism's inverted pyramid

Introduction

Lecture 1

Concepts

• computer - calculations, storage, result memorization, - tell them what to do! 
• 1. statement of facts  2. order/recipe/ the sequence of steps  
• flow of control: making decisions 
• 6 primitives --> types of result -- > instruction flow --> output 
• expression: primitives + programming languages
• expression - value - type 

[Revisit]

Programming

• 35:00
• give names, reuse names 
• = assignment (left - variable) 

Remaining Question: 

        usa_gold = 46
        uk_gold = 27
        romania_gold = 1
        total_gold = usa_gold + uk_gold + romania_gold
        print(total_gold)
        romania_gold += 1

    total_gold = usa_gold + uk_gold + romania_gold
    print(total_gold)

My question:

Why do we get 75 for the second print? 

My answer: 

From John's notes:    

  # radius = radius +1 is equal to radius += 1

so, romania_gold + = 1 is equal to romania_gold = romania gold + 1 

Hamlet Plot Analysis

In telling the story of a fatally indecisive character’s inability to choose the proper course to avenge his father’s death, Hamlet explores questions of fate versus free will, whether it is better to act decisively or let nature take its course, and ultimately if anything we do in our time on earth makes any difference. Once he learns his uncle has killed his father, Hamlet feels duty-bound to take decisive action, but he has so many doubts about his situation and even about his own feelings that he cannot decide what action to take. The conflict that drives the plot of Hamlet is almost entirely internal: Hamlet wrestles with his own doubt and uncertainty in search of something he believes strongly enough to act on. The play’s events are side-effects of this internal struggle. Hamlet’s attempts to gather more evidence of Claudius’s guilt alert Claudius to Hamlet’s suspicions, and as Hamlet’s internal struggle deepens, he begins to act impulsively out of frustration, eventually murdering Polonius by mistake. The conflict of Hamlet is never resolved: Hamlet cannot finally decide what to believe or what action to take. This lack of resolution makes the ending of Hamlet especially horrifying: nearly all the characters are dead, but nothing has been solved.

The play’s exposition shows us that Hamlet is in the midst of three crises: his nation is under attack, his family is falling apart, and he feels deeply unhappy. The Ghost of the old king of Denmark appears on the castle battlements, and the soldiers who see it believe it must be a bad omen for the kingdom. They discuss the preparations being made against the threat from the Norwegian prince, Fortinbras. The next scene deepens our sense that Denmark is in political crisis, as Claudius prepares a diplomatic strategy to divert the threat from Fortinbras. We also learn that as far as Hamlet is concerned, his family is in crisis: his father is dead and his mother has married someone Hamlet disapproves of. Hamlet is also experiencing an internal crisis. Gertrude and Claudius are worried about his mood, and in his first soliloquy we discover that he feels suicidal: “O that this too, too sullied flesh would melt” (I.ii.).

The three crises of the play’s opening—in the kingdom, in Hamlet’s family, and in Hamlet’s mind—lay the groundwork for the play’s inciting incident: the Ghost’s demand that Hamlet avenge his father’s death. Hamlet accepts at once that it is his duty to take revenge, and the audience can also see that Hamlet’s revenge would go some way to resolving the play’s three crises. By killing Claudius, Hamlet could in one stroke remove a weak and immoral king, extract his mother from what he sees as a bad marriage, and make himself king of Denmark. Throughout the inciting incident, however, there are hints that Hamlet’s revenge will be derailed by an internal struggle. The Ghost warns him: “Taint not thy mind nor let thy soul contrive/Against thy mother aught” (I.v.). When Horatio and Marcellus catch up to Hamlet after the Ghost’s departure, Hamlet is already talking in such a deranged way that Horatio describes it as “wild and whirling” (I.v.), and Hamlet tells them that he may fake an “antic disposition” (I.v.). The audience understands that the coming conflict will not be between Hamlet and Claudius but between Hamlet and his own mind.

For the whole of the second act—the play’s rising action—Hamlet delays his revenge by pretending to be mad. We learn from Ophelia that Hamlet is behaving as if he is mad with love for her. We see him make fun of Polonius by talking nonsense which contains half-hidden jokes at Polonius’s expense. Hamlet tells Rosencrantz and Guildenstern that he has “lost all [his] mirth” (II.ii.). Only at the end of Act 2 do we learn the reason for Hamlet’s delaying tactics: he cannot work out his true feelings about his duty to take revenge. First, he tells us, he doesn’t feel as angry and vengeful as he thinks he should: “I[…]Peak like John-a-dreams, unpregnant of my cause” (II.ii.). Second, he’s worried that the Ghost wasn’t really a ghost but a devil trying to trick him. He decides he needs more evidence of Claudius’s crime: “I’ll have grounds/More relative than this” (II.ii.).

As the rising action builds toward a climax, Hamlet’s internal struggle deepens until he starts to show signs of really going mad. At the same time Claudius becomes suspicious of Hamlet, which creates an external pressure on Hamlet to act. Hamlet begins Act Three debating whether or not to kill himself: “To be or not to be—that is the question” (III.i.), and moments later he hurls misogynistic abuse at Ophelia. He is particularly upset about women’s role in marriage and childbirth—“Why wouldst thou be a breeder of sinners?” (III.i.)—which reminds the audience of Hamlet’s earlier disgust with his own mother and her second marriage. The troubling development of Hamlet’s misogynistic feelings makes us wonder how much Hamlet’s desire to kill Claudius is fuelled by the need to avenge his father’s death, and how much his desire fuelled by Hamlet’s resentment of Claudius for taking his mother away from him. Claudius, who is eavesdropping on Hamlet’s tirade, becomes suspicious that Hamlet’s madness presents “some danger” (III.i.) and decides to have Hamlet sent away: Hamlet is running out of time to take his revenge.

The play’s climax arrives when Hamlet stages a play to “catch the conscience of the king” (II.ii.) and get conclusive evidence of Claudius’s guilt. By now, however, Hamlet seems to have truly gone mad. His own behavior at the play is so provocative that when Claudius does respond badly to the play it’s unclear whether he feels guilty about his crime or angry with Hamlet. As Claudius tries to pray, Hamlet has yet another chance to take his revenge, and we learn that Hamlet’s apparent madness has not ended his internal struggle over what to do: he decides not to kill Claudius for now, this time because of the risk that Claudius will go to heaven if he dies while praying. Hamlet accuses Gertrude of being involved in his father’s death, but he’s acting so erratically that Gertrude thinks her son is simply “mad […] as the sea and wind/When they each contend which is the mightier” (III.iv). Again, the audience cannot know whether Gertrude says these lines as a cover for her own guilt, or because she genuinely has no idea what Hamlet is talking about, and thinks her son is losing his mind. Acting impulsively or madly, Hamlet mistakes Polonius for Claudius and kills him.

The play’s falling action deals with the consequences of Polonius’s death. Hamlet is sent away, Ophelia goes mad and Laertes returns from France to avenge his father’s death. When Hamlet comes back to Elsinore, he no longer seems to be concerned with revenge, which he hardly mentions after this point in the play. His internal struggle is not over, however. Now Hamlet contemplates death, but he is unable to come to any conclusion about the meaning or purpose of death, or to resign himself to his own death. He is, however, less squeamish about killing innocent people, and reports to Horatio how he signed the death warrants of Rosencranz and Guildenstern to save his own life. Claudius and Laertes plot to kill Hamlet, but the plot goes awry. Gertrude is poisoned by mistake, Laertes and Hamlet are both poisoned, and as he dies Hamlet finally murders Claudius. Taking his revenge does not end Hamlet’s internal struggle. He still has lots to say: “If I had time […] O I could tell you— / But let it be” (V.ii.) and he asks Horatio to tell his story when he is dead. In the final moments of the play the new king, Fortinbras, agrees with this request: “Let us haste to hear it” (V.ii.). Hamlet’s life is over, but the struggle to decide the truth about Hamlet and his life is not.

MIT 6.0001 Problem Set 1

#1a:
annual_salary = float(input('Enter your annual salary: '))
portion_saved = float(input('Enter the percent of your salary to save, as a decimal:​ '))
total_cost = float(input('Enter the cost of your dream home: '))
current_savings = 0
portion_down_payment = 0.25
down_cost = total_cost * portion_down_payment 
r = 0.04
monthly_salary = annual_salary/12
num_months = 0

while current_savings < down_cost:
    current_savings += monthly_salary * portion_saved + current_savings * r/12
    num_months += 1

num_years = num_months/12  

print('Number of months:', num_months)
print('Number of years:',num_years)

#1b
annual_salary = float(input('Enter your annual salary: '))
portion_saved = float(input('Enter the percent of your salary to save, as a decimal:​ '))
total_cost = float(input('Enter the cost of your dream home: '))
semi_annual_raise = float(input('Enter the semi­annual raise, as a decimal: '))
current_savings = 0
portion_down_payment = 0.25
down_cost = total_cost * portion_down_payment 
r = 0.04
monthly_salary = annual_salary/12
num_months = 0

while current_savings < down_cost:
    current_savings += monthly_salary * portion_saved + current_savings * r/12
    num_months += 1
    if num_months%6 == 0:
        monthly_salary *= (1 + semi_annual_raise)

num_years = num_months/12   
    
print('Number of months:', num_months)
print('Number of years:',num_years)

#1c
def whatrate():
    annual_salary = int(input('Enter the starting salary: '))
    total_cost = 1000000
    semi_annual_raise = 0.07
    current_savings = 0
    portion_down_payment = 0.25
    down_cost = total_cost * portion_down_payment 
    r = 0.04
    monthly_salary = annual_salary/12
    num_months = 36
    high = 10000
    low = 0
    ans = (high + low)/2
    numofsteps = 0
    
    max_savings = 0
    for i in range(1,num_months+1):
        max_savings += monthly_salary + current_savings * r/12
        if i%6 == 0:
            monthly_salary *= (1 + semi_annual_raise)
    if max_savings < down_cost:
        return print('It is not possible to pay the down payment in three years.')

    min_savings = 0
    for i in range(1,num_months+1):
        min_savings += monthly_salary * 0.0001 + current_savings * r/12
        if i%6 == 0:
            monthly_salary *= (1 + semi_annual_raise)
    if min_savings > down_cost:
        return print('You don\'t really need to save, mate.')    
    
    while abs(current_savings - down_cost) > 100:
        current_savings = 0
        monthly_salary = annual_salary/12
        numofsteps += 1
        for i in range(1,num_months+1):
            current_savings += monthly_salary * ans/10000 + current_savings * r/12
            if i%6 == 0:
                monthly_salary *= (1 + semi_annual_raise)
        if current_savings > down_cost:
            high = ans
        else:
            low = ans
        ans = (high + low)/2
    print('Best savings rate:', round(ans/10000,4))
    print('Steps in bisection search:​', numofsteps)

Introduction to Psychology

Astrasum - User Growth

Current count: 89 + 346 = 435

Number of weeks: 10

Overall weekly growth rate: 34.7%

Global weekly growth rate: 17.2%

China weekly growth rate: 55.5%

27 Nov - Dec 3: 

• Global: 83 + 6
• China: 330 + 16
• Total: 413 + 22

20 Nov - Nov 26: 

• Global: 80 + 3   4%
• China: 323 + 7   2%
• Total: 403 + 10   2%

13 Nov - 19 Nov:

• Global: 78 + 2   3%
• China: 304 + 19   6%
• Total: 382 + 21   5%

6 Nov - 12 Nov: 

• Global: 71 + 7   10%
• China: 267 + 37   14%
• Total: 338 + 44   13%

30 Oct - 5 Nov:

• Global: 58 + 13   22%
• China: 202 +65   32%
• Total: 260 + 78   30%

23 Oct - 29 Oct:

• Global: 53 + 5   9%
• China: 168 + 34   20% 
• Total: 221 + 39   18%

16 Oct - 22 Oct:

• Global: 51 + 2   4%
• China: 125 + 43  34% 
• Total: 176 + 45   26%

9 Oct - 15 Oct:

• Global: 37 + 14   38%
• China: 95 + 30   32%
• Total: 132 + 44   33%

2 Oct - 8 Oct:

• Global: 30 + 7   23%
• China: 44 + 51  116%
• Total: 74 + 58   78%

25 Sept - 1 Oct:

• Global: 26 + 4   15%
• China: 31 + 13   42%
• Total: 57 + 17   30%

18 Sept - 24 Sept: 

• Global: 17 + 9   53%
• China: 4 + 27   675%
• Total: 21 + 36   171%