47
Two points moving together
Textbook: Part 2, lesson 47, pp. 25–27
GoalTwo points moving together: two points moving at the same time.
New words
together · birgalikdaat the same time · bir vaqtdastarting distance · dastlabki masofaapproaching · yaqinlashish
Explanation
If two points start at the same time, we find the coordinate of each separately. If A(5) moves right at 2 unit segments per second and B(30) moves left at 3, then after 4 s A is at 5 + 2 × 4 = 13 and B at 30 − 3 × 4 = 18. The distance between them is 18 − 13 = 5. Every second the distance shrinks by 2 + 3 = 5 unit segments.
Worked examples
After 4 s: A(13), B(18), AB = 5.
At first AB = 30 − 5 = 25; in 4 s it shrinks by 5 × 4 = 20: 25 − 20 = 5.
Class activity
“Two buttons”: move two buttons along a ruler ray at the same time with given steps and calculate the distance.
Practice
1
Point A(5) moves right at 2 unit segments per second. What is its coordinate after 4 s?
13
2
Point B(30) moves left at 3 unit segments per second. What is its coordinate after 4 s?
18
3
A(5) moves right at 2 and B(30) moves left at 3 unit segments per second. How many unit segments remain between them after 4 s?
5
4
Two points are 25 unit segments apart and approach each other at 2 and 3 unit segments per second. What is the distance after 4 s?
5