קישור להדפסת השאלה
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המשמעות היא שהמהירות גדלה בכל שנייה ב 4 מטר לשנייה.
חשוב להכיר את הגדרת המהירות , ואת משמעות היחידות של מהירות.
מהגדרת התאוצה, התאוצה מתארת בכמה גדלה המהירות בכל שנייה, לכן משמעות תאוצה של 4 מטר לשנייה בריבוע היא שהמהירות גדלה בכל שנייה ב 4 מטר לשנייה.
חשוב להבין כיצד מוגדרות היחידות הפיזיקליות. ולהבין את המשמעות של היחידות , של כל הגדלים הפיזיקליים.
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ביחס לציר שכיוונו ככיוון תנועת המכונית , וראשיתו במקום נמצא האופנוע ברגע t=0s .
ביטוי מקום המכונית בתלות בזמן הוא: x=87.5+30t.
ביטוי מקום המכונית בתלות בזמן הוא: x=87.5+30t.
יש להגדיר ציר תנועה , ולהשתמש בפונקציית המקום בתלות בזמן , המתאימה לתנועה במהירות קבועה . כדי לתאר את מיקום האופנוע ביחס לציר התנועה.
שני כלי הרכב נעים בכיוון זהה, נניח שהם נעים ימינה. נבחר ציר שכיוונו ככיוון תנועת כלי הרכב ימינה.
נמקם את ראשית הציר בנקודה בה נמצא האופנוע ברגע t = 0s.

המכונית נעה במהירות 108 קמ"ש , מהירות זו ביחידות תקניות שווה ל 30 מטר לשנייה(מחלקים ב 3.6).
המיקום ההתחלתי של המכונית ביחס לציר התנועה הנבחר הוא 87.5 מטר.
נתאר את מיקום המכונית בתלות בזמן , בעזרת פונקציית מקום זמן המתאימה לתנועה במהירות קבועה:
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נמקם את ראשית הציר במיקום בו נמצא האופנוע.
המכונית נעה במהירות קבועה שגודלה 108 קמ"ש , (נחלק גודל זה ב 3.6 כדי לבטא את המהירות ביחידות תקניות) השקולים ל 30 מטר לשנייה.
מיקומה ההתחלתי של המכונית ביחס לציר הנבחר הוא 87.5 מטר , נכתוב את פונקציית המיקום המתאימה לתיאור תנועת המכונית:
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האופנוע והמכונית בשאלה זו יכולים לנוע ימינה או שמאלה , ניתן לקבוע את כיוון תנועתם, ולהחליט על כיוון ציר תנועה , בהתאם לכיוון תנועת כלי הרכב ולכיוון הציר, נקבע ביטוי המקום בתלות בזמן. המהירות יכולה להיות חיובית או שלילית , למיקום ההתחלתי יכול להיות ערך כשלהו , אך הביטוי צריך להתאים לתנועה ביחס לציר הנבחר.
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ביחס לציר התנועה הנבחר, פונקצית המקום זמן המתאימה לתנועה האופנוע היא:
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האופנוע נע ממנוחה בתאוצה קבועה נתונה, יש להשתמש בפונקציית המקום זמן המתאימה לתנועה בתאוצה קבועה.
נכתוב את ביטוי המקום זמן ביחס לציר הנבחר.
המיקום ההתחלתי של האופנוע הוא 0 . האופנוע נע בכיוון הציר במהירות הולכת וגדלה, תאוצתו היא 2 מטר לשנייה בריבוע.
ביטוי המקום בתלות בזמן לתיאור תנועת האופנוע הוא:
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גודל תאוצת האופנוע לא תלויה בציר הנבחר , אך סימן התאוצה תלוי בכיוון הציר הנבחר.
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t=17.5s
שאלה זו עוסקת בתנועת שני גופים הנעים בזמני תנועה זהים, כדי למצוא את זמן המפגש, יש להשוות בין פונקציות המקום זמן של שני הגופים.
כדי למצוא את זמן המפגש , נגדיר את האופנוע כגוף 1, ואת המכונית כגוף 2. ונשווה בין שתי פונקציות המקום בתלות בזמן:
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התקבלה משוואה ריבועית, נסדר את המשוואה ונמצא את פתרונות המשוואה:
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אין משמעות פיזיקלית לזמן השלילי , לכן האופנוע ישיג את המכונית לאחר 17.5 שניות.
מתמטית ממשוואה ריבועית מתקבלים שני פתרונות, לכן למשוואת הזמן הריבועית יש שני זמנים. כאשר האופנוע נע בעקבות המכונית והא מתקרב אליה, יש רק רגע אחד בו לאופנוע ולמכונית יש ערך מיקום זהה. לכן בפתרונות המשוואה הריבועית חייבת להתקבל תשובה אחת חיובית ואחת שלילית. במידה והתקבלו שתי תשובות שליליות או שתי תשובות חיוביות, יש לבדוק את משוואות המקום זמן, ואת הפעולות המתמטיות בפתרון המשוואה הריבועית.
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המכונית נעה במהירות קבועה, האופנוע נע בתאוצה קבועה עד זמן המפגש, יש לתאר את תנועת שני כלי הרכב בגרף כמותי. לשם כך יש לחשב את מהירות האופנוע ברגע המפגש בעזרת פונקציית המהירות בתלות בזמן.
נחשב את מהירות האופנוע בעזרת פונקציית המהירות בתלות בזמן:
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לכן, ברגע המפגש t = 17.5s , מהירות האופנוע היא 70 מטר לשנייה.
מהירות המכונית קבועה, וגודלה 30 מטר לשנייה.
נתאר את תנועת האופנוע והמכונית בגרף מהירות בתלות בזמן:

אם לא צוין אחרת , יש לתאר את הגרף באופן כמותי, ולסמן בגרף ערכים חשובים . בשאלה זו כדי להשלים את כל ערכי הגרף החשובים, יש למצוא את מהירות האופנוע ברגע המפגש.
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