26
Motion problems
Textbook: Part 1, lesson 26, pp. 102–105
GoalKnow the formula S = v · t linking distance, speed and time and solve motion problems.
New words
speed · tezlikdistance · masofatime · vaqtkm per hour · km/h
Explanation
Speed is the distance covered in one unit of time. To find the distance multiply speed by time: S = v · t. The formulas v = S : t and t = S : v follow from the rule for an unknown factor. Speed is measured in km/h, m/min or m/s; the units of speed, distance and time must match. For example, if v = 70 km/h, in 3 hours S = 70 × 3 = 210 km. It is convenient to write a problem as “Given”, “Solution”, “Answer”.
Worked examples
A train at 70 km/h covers 350 km in t = 350 : 70 = 5 hours.
A cyclist rode 60 km in 4 hours. His speed is v = 60 : 4 = 15 km/h.
Class activity
“Speed of steps”: pupils walk 10 steps in the classroom, time themselves in seconds and calculate steps per second (only in the classroom, carefully).
Practice
1
A cyclist rode at 12 km/h for 5 hours. How many km did he cover?
60
2
How many hours does a car at 80 km/h need for 240 km?
3
3
A pedestrian walked 350 m in 5 minutes. What is the speed in m/min?
70
4
Tashkent to Samarkand is about 300 km. How many hours does a bus at 75 km/h need? Why do we divide?
4 hours. Because t = S : v: 75 km is covered each hour, and 300 km holds 300 : 75 = 4 such parts.