Examples for secondary school students - page 130 of 230
Number of problems found: 4582
- Acceleration 7074
A ball placed on an inclined plane begins to move and reaches a speed of 1 m/s in 5 s. Assuming that the ball's motion is uniformly accelerated, determine the magnitude of its acceleration and the distance it travels in the given time. - An acceleration
The car goes on a straight road at a speed of 72 km/h. At some point, the driver starts to brake and stops the car in 5 seconds. Find: (a) the acceleration during braking and (b) the distance traveled during braking. - Acceleration 7071
A tractor travels along a straight road at a speed of 15 m/s. The tractor driver starts braking with an acceleration of 2 m/s². Specify a) the magnitude of the speed and the path of the tractor in 5 s from the moment it started to brake b) the time for wh - Train speed
The train speed is decreased from 72 km/h to 36 km/h in 50 seconds. If the train movement is continuously slowing, find the acceleration and the distance it travels. - The crime
The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in 1990 and the crime rate remains constant each year, determine the approximate number of crimes in 2025. - Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that: a) only boys went on the field trip b) just 2 boys went on the field trip - Collision
The two bodies, whose initial distance is 240 m, consistently move evenly against each other. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s². The second body has an initial speed of 6 m/s and an acceleration of 2 m/s². Find
- Car crash
A car crash occurred on the road with a maximum permitted speed of 60 km/h. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, assu - Acceleration 7054 The car brakes with an acceleration of 5 m/s². Determine the stopping distance of the car if its initial speed is a) 54 km/h, b) 108 km/h. Compare the calculated braking distances concerning the given speeds.
- AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area? - Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm - The tourist
The tourist traveled 190km in 5 hours. Part of the journey was at 5 km/h, and the rest was by bus at 60 km/h. How long has a bus gone? - Positive 7040
Find all positive integers x and y for which: 1 / x + 1 / y = 1/4 - Younger 7033
Cyril was four times less than Dalibor 3 years ago. How many years will Cyril be 2x less if he is 3x younger now?
- Linear system
Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2 - Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if the distance of the pavement from the center is 15 m. - Diagonals 7029
The number of diagonals of a given polygon is 88 more than the number of its sides. How many sides does this polygon have - Two diggers
Two diggers should dig a ditch. If each of them worked one-third of the time the other digger needed, they'd dig up a 13/18 ditch together. Find the ratio of the performance of these two diggers. - Notation 7014
There is no 0 in the decimal notation in natural numbers; there are even numbers or odd numbers, each at least once. Find the number of all k-digit natural numbers.
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