Motion In One Direction PDF

Mr. Khaled Yossry contact : 01069655370 Change in an object position as time passes according to the position of another fixed object. The simplest type of motion is Motion in a straight line. The motion of the train and m...

Mr. Khaled Yossry contact : 01069655370 Change in an object position as time passes according to the position of another fixed object. The simplest type of motion is Motion in a straight line. The motion of the train and metro are examples of motion in one direction. G.R Because the metro or train are moves forward or backward in straight path or curved path of combination of both of them but they don’t move up or down If two cars move on the same path. The 1st car covered 10 km in 2 minutes. The 2nd car covered the same distance (10 km) in 5 minutes. 1st car 10 km covered in 2 minutes Initial Final position position 2nd car 10 km covered in 5 minutes The 1st car is faster because it covered the same distance in a shorter time Two objects cover a certain distance in different intervals of time, because they are moving with different speeds. The object which spends the least time has the highest speed. If 2 persons are riding their bikes along the same path 1 Mr. Khaled Yossry contact : 01069655370 The 1st biker covered 100 m & the 2nd covered 200 m. Both took the same time. Which one has the highest speed? 100 m The speed of the 2nd biker is bigger because he covered a longer distance in an interval of time equal to the 1st biker. 200 m Conclusion The speed of the moving object depends on 2 factors: A- The distance covered. B- The time taken. Speed: It is the distance moved through a unit time. It is the rate of change of distance. The object speed increases by decreasing the time taken to cover a certain distance. Because V = d/t so, The object speed is inversely proportional to time taken when the distance is fixed. The object speed increases by increasing the covered distance at a certain time. Because V= d/t so the object speed is directly proportional to covered distance when the time is fixed. Distance (d) The measuring units Speed (V) = of speed are km/h or m/s Time (t) 1 km = 1000 m 1 hour = 60 minute 1 minute = 60 seconds 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎𝟎 𝟏𝟎 𝟓 Speed "km/h" X = = = = Speed "m/s 𝟔𝟎 𝑿 𝟔𝟎 𝟔𝟎 𝑿 𝟔𝟎 𝟑𝟔 𝟏𝟖 𝟓 (Multiply the value of the speed "km/h" X to get the speed value in m/s) 𝟏𝟖 Ex: A car moves at 20 m/sec. 20 ÷ 5/18 = 72 Km/h. Ex: A car moves at 90 km/h. 90 X 5/18 = 25 m/sec. 2 Mr. Khaled Yossry contact : 01069655370 A sprinter runs at a speed of 6 m/sec. find the distance covered by the runner in 10 seconds. Solution: Distance (d) = speed (V) x time (t) d = 6 x 10 = 60 Meters A train covers 50 meter in two seconds find speed in km/h Solution: Speed (V) = distance (d) /time (t) = 50/2 = 25 m/sec. 25 ÷ 5/18 = 90 Km/h A plane moves from Aswan airport & covers a distance of 850 Km in 1 hour to reach cairo airport. Calculate the speed at which the plane moves in: 1.Km/h. 2. m/sec. Solution 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 (𝑲𝒎) 1- The speed of plane in (Km/h.) = = 850 / 1 = 850 Km/h. 𝒕𝒊𝒎𝒆 (𝒉𝒐𝒖𝒓) 2- The speed of plane in (m/sec.) = speed in Km/h. X 5/18 = 850 x 5/18 = 236.1 m/sec. A train starts to move at 6 o'clock in the morning, then what is the time of arrival if it moves at speed of 40 km/h to cover a distance of 200 km? Solution Time (t) = distance (d) /speed (V) = 200/40 = 5 hours. The time of arrival = 6 + 5 = 11 so the train arrival is eleven in the morning. Cars & planes are provided by speedometer. G.R To help us in identifying the speed of car & planes directly. 3 Mr. Khaled Yossry contact : 01069655370 The car in the figure covers 20 m in the 1st second & 20 m in the 2nd second & another 20 m in the 3rd second and so on if it completes its motion. So, Regular (uniform) speed The speed in which the object covers equal distances in equal intervals of time. The speed is non-uniform when a moving object covers equal distances in variable intervals of time. 1 second 2 second 3 second 10 m 10 m 10 m When a moving object covers variable distances in equal intervals of time, its speed is non-uniform. 1 second 1 second 1 second 10 m 20 m 30 m So, Irregular (non-uniform) speed The speed in which the object covers unequal distances in 1 second 1 second 1 second equal intervals of time or vice versa. 20 m 20 m 20 m 4 Mr. Khaled Yossry contact : 01069655370 Most of moving cars cannot move inside crowded towns all time by uniform speed. Because the speed of the car changes according to the conditions of road & the traffic. The metro moves at irregular speed. Because the Metro covers unequal distances at equal periods of time or covers equal distances at unequal periods of time. Calculate the distance covered by car which moves at regular speed of 70 Km/h during: a- Half an hour b- Two hours Solution: Speed V = distance d/time t d= V x t a- d = 70 X 1/2 = 35 km b- d = 70 X 2 = 140 km A body moves in a straight line at regular speed & the distance covered in different times is recorded in the following table: Distance (m) 10 20 (X) 40 50 60 Time (sec.) 5 10 15 20 (Y) 30 1- Calculate speed of the body? 2- What is the value of X & Y ? Solution speed (V) = Distance (d) / Time (t) = 10/5 = 20/10 = 40/20 =2 m/sec. distance (X) = V X t = 2 X 15 = 30 m time (Y) = d/V = 50 / 2 = 25 sec. Electromagnetic waves such as light transfer through the space with a constant speed equals 3 x 108 m/sec. The time needed for the sun light to reach the earth is determined by: Speed of light = Distance / Time Where, distance between The Sun & The Earth equals 149 million Km. Since, speed of light = 300 000 Km/sec. so, time needed for sunlight to reach the Earth (t) = d/v = 149 x 106 / 300 000 = 497 sec. = 8 minutes & 17 seconds 5 Mr. Khaled Yossry contact : 01069655370 6:00:00 - 00 : 08 : 17 = 05 : 51 : 43 Time of Time needed for sun The time at which the sunlight sunrise light to reach the earth travelled from the sun. Consider a car trip from your home to a place 100 km away along a straight road. An hour was needed to reach your distance but you probably decreased your speed at certain moments then stopped in front of a red light then increased your speed again. Your speed through the trip is non-uniform. Your average speed through the whole trip = Total distance covered ÷ Total time taken. Therefore the average speed of this trip = 100km/1hour = 100 km/h Total Distance covered (d) Average Speed (V) = Total Time (t) The average speed is: The total distance covered by the moving object divided by the total time taken to cover this distance. The regular speed by which the object moves to cover the same distance at the same period of time. 6 Mr. Khaled Yossry contact : 01069655370 A racer covered a distance of 100 meters of a straight track in 10 seconds, then returned back walking, he took 80 seconds to come back to starting point of running. Calculate the racer's average speed: 1- While running. 2- While returning. 3- During the whole trip. Solution 1- The racer's average speed while running V = d//t = 100/10 =10m/sec 2- The racer's average speed while returning V = d/t = 100/80 = 1.25 m/s 3- The racer's average speed during the whole trip V = d/t = 100+100/80+10 = 200/90 = 2.2 m/s A sprinter covered the first 100 meters of the race at 10 seconds & the last 300 meters of the race at 40 seconds, Find in which part of the race did he have the highest average speed? Then , Calculate his average speed during the whole trip. Solution The runner's average speed during the first 100 m V = d/t = 100/10 = 10m/s The runner's average speed during the last 300 m V = d/t = 300/40 = 7.5m/s The runner's average speed in the 1st 100 m was faster than that in the last 300 m. The runner's average speed during the whole trip V = d/t = 100+300/10+40 = 400/50 = 8 m/s ❖ The object moves with regular motion when its constant speed = its average speed. V=V And the speed in this case is called regular speed of an object ❖ The object moves with irregular motion when its constant speed ≠ its average speed. V≠V And the speed in this case is called irregular speed of an object 7 Mr. Khaled Yossry contact : 01069655370 The diagrams below show two cars moving along the same straight road. The speed of car B is 30 m/s & the speed of car A is 40 m/s. For an observer who is in car B , the speed of car A is only 10 m/s. Measuring the speed depends on the position of the observer who is determining the magnitude (value) of the speed. Relative speed The relative speed of a moving object in a certain direction differs according to the difference of the observer state & the direction of its movement: A- Object & Observer moves in the same direction at different speed. Observer Object 50 km/h 100 km/h The relative speed = the real speed of the object – the observer's speed The real speed of the object = The relative speed of the object + The observer's speed. The relative speed is Less than the real speed. B- Object & Observer move in the same direction at same speed. Observer 100 Km/h 100 Km/h Object The relative speed = The difference between the two speeds = zero. 8 Mr. Khaled Yossry contact : 01069655370 The object seems static. C- Object is in motion & the Observer is at rest. Observer Object 0 Km/h 60 Km/h The relative speed = the real (actual) speed of the object. D- Object and observer move in opposite directions. Observer Object 60 Km/h 100 Km/h The relative speed = the real speed of the object + the observer speed The real speed of the object = the relative speed of the object – the observer speed The relative speed is More than the real speed. When does the relative speed of a moving object relative to an observer equal to double of its real speed ? This occurs when the observer moves in the opposite direction at the same speed of the moving object When does the relative speed of a moving object relative to an observer equal to zero? This occurs when the observer moves in the same direction at the same speed of the moving object. 9