Unit 1 Physics and Chemistry Kinematics

Size: px

Start display at page:

Download "Unit 1 Physics and Chemistry Kinematics"

Adela Lawson
5 years ago
Views:

1 4 th ESO. UNIT 1: KINEMATICS Kinematics is a branch of Physics which describes the motion of bodies without regard to its causes. A reference frame is a set of coordinate axis in terms of which the position of the body in motion may be specified. Trajectory is the path that a moving object follows through space as a function of time. Position is a vector magnitude which informs about the location of the moving body in a specific moment in reference to the chosen reference frame. Distance is a scalar magnitude that informs about how much ground an object has covered between two points. Displacement is a vector that informs about the change in position in a period of time. Speed and velocity Average speed is a scalar quantity which is the relationship between distance and time. It is measured in metres per second. Speed is the rate of change of distance and refers to how fast a particle is moving: a fast-moving particle has high speed and covers large distances in a short interval of time. On the other hand, zero-speed means a state of rest. Generally speaking average speed is not the same speed at which an object is moving. When we define the average speed through an infinitesimal (very, very, very, very short) interval of time we get the actual speed of the object, in other words, the instantaneous speed. 1

2 Velocity is a vector quantity, which means that is direction aware. Therefore, velocity is the speed with a direction. Acceleration When a particle is moving, it usually undergoes changes of velocity: it can speed up, it can change of direction or it can slow down. It is very important to measure the changes of velocity so as to know the type of motion. Acceleration is a vector quantity which refers to the rate of change of velocity. It is defined as the relationship between the change of velocity and the time taken. Notice that it is directly proportional to the change of velocity and inversely proportional to the time taken. It is measured in metres per second squared. Generally speaking average acceleration is not the same acceleration an object has all the time. When we define the average acceleration through an infinitesimal (very, very, very, very short) interval of time we get the actual acceleration of the object, in other words, the instantaneous acceleration. Uniform linear motion (ULM) Uniform linear motion (ULM) is motion along a straight line which has constant velocity. As its velocity is constant, it has zero-acceleration. A body which is moving at constant velocity travels the same distance each time interval. In this motion, the average speed in any interval of time is the same as the instantaneous speed at any time. Linear uniformly accelerated motion (LUAM) Uniformly accelerated motion is a motion along a straight line which has constant acceleration. Uniform circular motion (UCM) Uniform circular motion is a motion through a circumference at the same rate. In other words, the particle covers the same distance each interval of time. Notice that the speed of the motion is always the same, but velocity changes because of the change of direction along the circumference. 2

3 The angles are measured in radians. One radian is the angle which has the length of its arc equal to its radius. IMPORTANT: 2 rad=360º=1 revolution If =1 rad, s=r Despite moving at the same speed, a particle with a circular uniform motion has acceleration, because the direction of velocity changes as time passes. This acceleration is called centripetal acceleration and acts towards the centre of the circle. The time needed to complete one revolution is called period (T). The number of revolutions made in 1 second is called frequency (f). Average speed EXERCISES 1. A girl rides a bike and travels 4 km in 10 minutes. Calculate its average speed in m s -1 and km h A body has constant velocity. Its position throughout time is shown in the following table: Position (m) a) Plot the graph position vs time. b) Calculate the average speed in the intervals from 0 to 1 s, from 2 to 4 s and from 0 to 5 seconds. 3. A car travels at 75 km h -1 through a road. Calculate the time needed to cover a distance of 130 km. Express the speed in m s -1 and calculate the distance travelled in 20 minutes. 4. Order these velocities from the slowest to the highest: a) 72 km/h b) 1200 km/day c) 3563 dm/min d) 30 m/min e) 15 cm/s 5. Which of these animals is the fastest? Which one is the slowest? Sloth bear: 0 2 km/h snail: 5000 cm/h turtle: 70 m/h 6. Speed limits in UK are 30, 50 and 70 miles per hour. Convert these limits in km h -1 and m s -1. Use conversion factors. [1 mile=1609 metres] 3

4 7. A body has constant acceleration. Its position throughout time is shown in the following table: Position (m) a) Plot the graph position vs time. b) Calculate the average speed in the intervals from 0 to 1 s, from 1 to 2 s, from 2 to 3 s, from 3 to 4 s, from 4 to 5 s and from 0 to 5 seconds. 8. Anna needs 40 minutes to arrive to her high school, which is 3 km away from her home. She stays at school for 7 hours and then comes back walking, but she is more tired than she was in the morning and spends 50 minutes walking home. Plot the graph space vs time and speed vs time. Consider that in each step her velocity is constant. 9. A car leaves town A at 4 p.m. and arrives to town B, where it stops, at 5.45 pm. At 6.45 p.m., the car continues the trip and arrives to town C at 8.15 p.m. If the distance between A and B is 189 km, and between B and C is 135 km, calculate the medium velocity: a) in the trip from A to B; b) in the trip from B to C; c) in the whole trip. Express the solution in SI units. Average acceleration 10. A woman travels in her car at 90 km h -1 and she accelerates to 120 km h -1 in 4 seconds. Calculate her acceleration in m s A car moves in the city with a speed of 50 km/h. When it reaches a red light, it slows down until it stops. It takes 1 second to stop. What is the acceleration of this car? Uniform Linear Motion (ULM) 12. The distance from Madrid to Córdoba is 401 km. If you travel to Córdoba from Valdemoro (which is located between Madrid and Córdoba at a distance of 28 km from Madrid), with a constant speed of 90 km/h, calculate the time you need to arrive there. 13. Andrew starts walking from home to school at a medium velocity of 6 m/s. If the school is 900 m away, how long will it take him to get there? 14. A body has a uniform linear motion with a speed of 8 m/s. Complete the following table and draw the graph space vs time: t (s) s (m) 15. A bird flies at a speed of 15 m/s. Make a table with the position of the bird every 5 seconds for the first 40 seconds. Draw the graph of displacement versus time using the table you have made. 16. Describe the type of motion in each of the parts of the graphic: 4

5 17. Describe the type of motion in each of the parts of the graphic: Linear Uniform Accelerated Motion (LUAM) 18. Find the constant acceleration needed to allow a car to accelerate in a straight line from a speed of zero to a speed of 30 m/s in 5 s. 19. An airplane must reach a takeoff speed of 80 m/s in a 1000 m long runway. What minimum constant acceleration is required? 20. A body starting from rest acquires a velocity of 200 m/s in 10 seconds. Calculate the acceleration and the distance travelled by the body in 10 seconds. 21. A body starts moving with a velocity of 40 m/s and an acceleration of 10 m/s 2. Find the distance travelled by the body in 15 seconds and the velocity at the end of the 15 th second. 22. A driver who is moving at 20 m s -1 notices a huge rock on the road, and it takes him 4 seconds to stop his car. Calculate the acceleration and the distance travelled. If the rock was located at a distance of 45 m when he saw it, did he have time to avoid crashing the rock? 23. A car increases its speed from 60 km/h to 80 km/h in 6 seconds. Calculate its acceleration, the speed it will have 9 seconds after starting accelerating and the distance it will have travelled in the 9 seconds (suppose the acceleration remains constant). 24. When approaching the station, a train which initially moved at 110 km/h slows down until it stops. If the acceleration was -1.5 m/s 2, how long did it take the train to stop? What was the distance from the station when the train began to slow down? 25. A body at rest starts moving with an acceleration of 3 m/s 2. Complete the following tables and plot the graphs space vs time and speed vs time: Speed (m/s) Space (m) 26. A body with an initial speed of 1 m s -1 accelerates 2 m s -1 each second. Draw the graphs space vs time and speed vs time for the first 8 seconds. 27. A body which moves with a speed of 20 m/s slows down with an acceleration of -2.5 m s -2. Plot the graphs space vs time and speed vs time for every second until it stops. 5

6 Catch up with exercises 28. A car moves at 120 km/h. Another car, located 3 km ahead, moves at 80 km/h in the same direction as the first car. When and where will the first car catch up with the second car? Draw one graph space-time with the motion of the two cars. 29. A car travels at 85 km/h. Another car, located 8 km ahead, moves at 100 km/h but in opposite direction, towards the first car. Calculate when and where will these cars meet. Draw one graph space versus time with the motion of the two cars. 30. Two trains are located 2000 m apart. Train one is moving with a constant speed of 30 m/s directly towards train 2 which starts from rest and accelerates with a constant acceleration of 5 m/s 2 directly towards train 1. When will the trains meet? 31. When a traffic light turns green, a car crosses it with a constant speed of 40 km/h. Two seconds later, another car that was at rest at the traffic light starts moving with an acceleration of 2 m/s 2. When will the second car catch up with the first car? What will be the distance from the street light then? 32. Carlos, who is in Pinto, starts driving to Getafe with a constant speed of 70 km/h. At the same time, Sandra, who is in Getafe, starts driving to Pinto with a constant speed of 80 km/h. When will they meet? Where? The distance between Getafe and Pinto is 12.8 km. Take the reference frame in Pinto. Free fall motion 33. A body is vertically thrown up from the floor with an initial speed of 25 m/s. Calculate: a) The time it will need to reach the maximum height. b) The maximum height. c) The time it will need to reach the ground again. d) The speed at which it will reach the ground. 34. You drop an object from an initial height of 10 m. Calculate the time it takes to strike the ground. 35. An object is dropped from a height of 75 m. Calculate the position and the speed of the object 2 seconds later. 36. An apple is vertically thrown down with a speed of 4 m/s from the top of a building which is 101 m high. Calculate the time it will take for the apple to reach the ground and the velocity it will have at that moment. 37. A ball is dropped from a height of 100 m above ground level. Neglect the effects of air resistance. a) What is the velocity of the ball one second after it has been dropped? b) How long will it take the ball to strike the ground? c) What is the velocity of the ball when it strikes the ground? 38. A ball thrown straight up in the air reaches a height of 30 m above the level from which it was thrown. What was the velocity of the ball when it left the hand of the thrower? What was the velocity of the ball 1.5 seconds after it was thrown? 39. A flower pot falls from a balcony which has a height of 20 metres. Calculate when it will strike the ground and its velocity then. 40. From a height of 4 metres a ball is thrown vertically up with a speed of 6 m/s. Calculate: a) The maximum height. b) The speed when it strikes the ground. 41. A coin is dropped in a well and it reaches the bottom in 4 seconds. Calculate the depth of the well. 6

7 Uniform Circular Motion (UCM) 42. A cyclist moves with a constant speed of 15 m/s on a circular track whose radius is 50 m. Calculate: a) Its angular speed in rad/s and in rpm. b) The angle the cyclist will have covered in 45 seconds. c) The distance the cyclist will have travelled in 45 seconds. d) The centripetal acceleration. 43. A body moves with a circular motion with an angular speed of 30 rpm. The radius of the circumference that is described is 40 cm. Calculate: a) The angular speed in rad/s. b) The linear speed in m/s. c) The linear speed in km/h. d) The distance the body will have travelled in 1 minute. e) The centripetal acceleration of the body. 44. A disc whose diameter is 25 cm rotates at 20 rpm. Calculate: a) Its period and frequency. b) The linear speed of a peripheral point. 45. The satellite Europa rotates around Jupiter with an average speed of m/s. The average distance between the center of Europa and the center of Jupiter is km. Calculate: a) The angular speed of this motion in rad/s. b) The period and the frequency of this motion. 46. The period of the Earth orbiting the Sun is days (this 0.25 is the reason there is a leap year every four years). If the linear speed of the Earth around the Sun is km/s, calculate the average distance between the center of the Sun and the center of the Earth. 47. In a uniform circular motion, a body rotates an angle of 2.1 radians travelling a distance of 6 metres in 0.25 seconds. What is the radius of the circumference? What is the linear speed? 48. The frequency of a disc is 1.2 Hz and its diameter is 45 cm. Calculate its angular and linear speed and the angle it will have rotated in 2 minutes. 49. The angular speed of a circular motion, whose diameter is 15 m, is 2 rpm. Calculate: a) The angular speed in rad/s. b) The linear speed in m/s and in cm/min. c) The angle, in rad, the body will have rotated in 3.7 minutes. 50. The distance between the centers of the Moon and the Earth is km and the time the Moon needs to complete a revolution around the Earth is 29.5 days. Calculate the angular speed and the linear speed of the Moon. 7

Kinematics. 1. Introduction to Kinematics. 2. Position and displacement

Kinematics. 1. Introduction to Kinematics. 2. Position and displacement Kinematics 1. Introduction to Kinematics. Scalars & vectors 2. Position & displacement 3. Velocity 4. Acceleration 5. Uniform linear motion 6. Uniformly accelerated motion 7. Uniform circular motion 1.