Physics Lesson 1: Motion in One Direction PDF

# Lesson 1: Motion in One Direction ## What is meant by motion? - Motion happens all around us. Everyday, we see objects such as cars and motorbikes move in different directions at different speeds. - When the position of an object (as a bike) changes as time passes according to the position of an...

# Lesson 1: Motion in One Direction ## What is meant by motion? - Motion happens all around us. Everyday, we see objects such as cars and motorbikes move in different directions at different speeds. - When the position of an object (as a bike) changes as time passes according to the position of another fixed object (as a traffic light), we can say that the first object (the bike) is in a state of motion. ## Motion It is the change of an object position (location) as time passes according to the position of another fixed object. - To simplify the concept of motion, we will study the motion in one direction, whether the path of a moving object: Straight or curved or combination of both. - The simplest type of motion is the motion in a straight line in one direction. - **Example:** The motion of the train or the metro. ## The motion of a train is considered as an example of motion in one direction. Because the train moves forward or backward in a straight path or curved path or combination of both. ## But, how can we describe and compare the motion of objects? ### Speed - We can describe the motion of some objects around us as fast and some others as slow. - Speed is a physical quantity which is used to describe and compare the motion of objects. - If there are two cars, one of them is Red and the other is Blue, which of them is faster in the following two cases? #### The first case If the two cars move for the same period of time which is 5 sec. - The Red car covers a distance of 100 m. - The Blue car covers a distance of 50 m. #### The second case If the two cars cover the same distance which is 100 m. - The Red car takes a time 5 sec. - The Blue car takes a time 10 sec. We find that the Red car is faster than the Blue car because the Red car covers large distance (100 m.) in the same time (5 sec.) while the Red car takes less time (5 sec.) to cover the same distance (100 m.). ## From the previous explanation, we conclude that: The two factors necessary for the description of speed (motion) are: 1. The distance covered by the moving body. 2. The time taken by the moving body to cover this distance. ## We can define speed as follows: - Speed is the distance moved through a unit time. - Speed (V) = Distance (d) / Time (t) - It is also the rate of change of distance. ## To calculate Speed, Distance and Time: | Speed | Distance | Time | | --------------- | ---------------- | ---------------- | | V = d / t | d = V x t | t = d / V | | | | | ## When the following happens...? - The amount of the object speed is equal to the amount of the distance covered. - When the object covers this distance through a unit time (1 hour or 1 minute or 1 second) **G.R.** - 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 the time taken, when the distance is constant. - 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 the covered distance, when the time is constant. ## The measuring units of speed - The speed measuring unit is different according to the units of distance and time which are used, as in the following: ### Measuring units of distance - 1 kilometre = 1000 metres - 1 metre = 100 centimetres - 1 kilometre = 1000 x 100 = 100000 centimetres ### Measuring units of time - 1 hour = 60 minutes - 1 minute = 60 seconds - 1 hour = 60 x 60 = 3600 seconds ### Measuring units of speed - For illustration: - 1 kilometre / 1 hour = 1000 metres/60 x 60 seconds = 10/36 = 5/18 m/sec. - **Ex.1:** A car moves at 72 km/h. - 72 x 5/18 = 20 m/sec. - **Ex.2:** A car moves at 20 m/sec. - 20 ÷ 5/18 = 72 km/h. ## Note To compare the speed of two objects, the measuring units must be the same. # Problems ## 1. A runner runs at a speed of 6 m/sec. Find the distance covered by the runner in 10 seconds: ### Solution V = d/t ..d=Vxt d=6x10= 60 metres. ## 2. A train covers 50 metres in two seconds, find its speed in km/h. ### Solution V = d/t = 50/2 = 25 m/sec. V = 25 x (5/18) = 90 km/h. ## 3. A train starts to move at 6 o'clock in the morning. What is the time of arrival, if it moves at a speed of 40 km/h to cover a distance of 200 km ? ### Solution V d/t .. t = d/V = 200/40 = 5 hours. The time of arrival = 6 + 5 = 11. .. The train arrival is eleven in the morning. ## Question 1. Solve the following problem. - A plane moves from Cairo airport and covers a distance of 3200 km in 5 hours to reach Paris airport. Calculate the speed at which the plane moves in (km/h) and in (m/sec.). 2. Complete the following sentences: - A. If the object covers 10 km in 30 minutes, this means that its speed = \[... km/h.\] - B. If the object covers the same distance in a longer time, this means that its speed becomes \[... .\] ## What is meant by ...? - A car moves at a speed of 120 km/h. - This means that the car covers a distance of 120 kilometres in one hour. - A train covers a distance of 150 km in two hours. - This means that the train moves at a speed equals 75 km/h. - Where, V = d/t = 150/2 = 75 km/h. - The speed of a car equals zero. - This means that the car is at rest. # NB: Cars and planes are usually provided with a group of counters such as speedometer, mileage, hour timer and compass. **Ex.:** If the car speedometer pointer points to 7, this means that the car speed is 7 km/h. (= 20 m/sec.). **G.R.**Cars and planes are provided by speedometer. To help us in identifying the speed of car and planes directly. ## Speed can be described as: ### Types of Speed Regular (uniform) speed | Irregular (non-uniform) speed **What is the difference between them?** | Time (sec.) | Distance (m.) | | Time (sec.) | Distance (m.) | | ------------- | ------------- | ---- | ------------- | ------------- | | 00:10 | 100 | | 00:10 | 100 | | 00:10 | 100 | **A** | 00:10 | 120 | | 00:10 | 100 | | 00:10 | 80 | | 00:10 | 100 | | 00:10 | 100 | **From the previous two figures, we conclude that:** - **The car A** moves to cover equal distances (100 m.) at equal periods of time (10 sec.). - So, the car moves at a regular (uniform) speed. **-Regular (uniform) speed:** - It is the speed by which the object moves when it covers equal distances at equal periods of time. - **The car B** moves to cover unequal distances (100, 120, 80 m.) at equal periods of time (10 sec.). - So, the car moves at an irregular (non-uniform) speed. **-Irregular (non-uniform) speed:** - It is the speed by which the object moves when it covers unequal distances at equal periods of time. - Or it is the speed by which the object moves when it covers equal distances at unequal periods of time. **Think? What is the thing that moves at a constant speed in the space?** All electromagnetic waves such as light transfer through the space with a constant speed equals 3 × 10⁸ m/sec. ## What is meant by ...? - An object moves at a regular speed of 50 km/h. - This means that the object covers a distance of 50 kilometres each one hour. **G.R** - Most of moving cars cannot move inside crowded towns all the time by uniform speed. Because the speed of the car changes according to the conditions of the road. - The metro moves at an irregular speed. Because the metro covers unequal distances at equal periods of time, or it covers equal distances at unequal periods of time. # Problems ## 1 Calculate the distance covered by a car, which moves at a regular speed of 70 km/h during: 1. Half an hour. 2. Two hours. ### Solution V = d/t ..d=Vxt 1. d = 70 x(1/2) = 35 km. 2. d=70 x 2 = 140 km. ## 2 A body moves in a straight line at a regular speed and the distances covered in different times is recorded in the following table : | Distance (m) | Time (sec.) | | ------------- | ------------- | | 10 | 5 | | 20 | 10 | | 40 | 15 | | 50 | 20 | | 60 | 30 | 1. Calculate the speed of the body. 2. What is the value of (X) and (Y) ? ### Solution 1. Speed (V) = Distance (d) / Time (t) = 10/5 = 20/10 = 40/15 = 60/30 = 2 m/sec. 2. - Distance (X) = Speed x Time = 2 x 15 = 30 m. - Time (Y) = Distance / Speed = 50/2 = 25 sec. ## 3 From the following figure, does the person move at a regular speed or at an irregular speed? Why? || |---|---| | 1 sec. | 2 sec. | | 1 sec. | 3 sec. | | A | B | | 1m | 3m | | 4m | 7m | ### Solution - d1/t1 = 1/1 = 1 m/sec. - d3/(t3) = 1/1 = 1 m/sec. - d2/t2 = 2/2 = 1 m/sec. - d4/(t4) = 3/3 = 1 m/sec. .. V1 = V2 = V3 = V4 So, the person moves at a regular (uniform) speed as he covers equal distances (1 metre) at equal periods of time (1 sec.). ## TRY to answer worksheet 1 in the Notebook ## Average Speed - It is difficult to determine the amount of irregular speed of the object, so we use another term which is called "Average speed". ### Average speed: It is the total distance covered by the moving object divided by the total time taken to cover this distance. **Average speed can be calculated as follows:** Average speed (V) = Total distance (d) / Total time (t) V = (d1 + d2 + d3 + ... ) / (t1 + t2 + t3 + ... ) ## What is meant by …? - The average speed of a moving car is 40 km/h. - This means that the total distance covered by the car through one hour equals 40 km. ## When the following happens...? - The value of average speed of a moving body equals to its speed at any moment (V = V). - When the body moves at a regular speed. - The value of average speed of a moving body differs from the value of its speed at any moment (VV). - When the body moves at an irregular speed. ## Relative Speed *If there is a person standing on the side of the road (called the observer) to observe two cars (A & B), the car (A) moves at 100 km/h and car (B) moves at 80 km/h in the same direction. **Therefore:** - The speed of car (A) relative to the static observer = 100 km/h. - The speed of car (B) relative to the static observer = 80 km/h. - The speed of car (A) relative to an observer in car (B) =100-80 = 20 km/h. | **Static observer** | **80 km/h** | **100 km/h** | | --------------------- | ----------- | ----------- | | | B | A | **Notes: ** - The speed of car (A) relative to the static observer differs from its speed relative to an observer in car (B). - Measuring the relative speed depends on the position of the observer who determines the magnitude of this speed. **- Relative speed:** It is the speed of a moving object relative to a static or a moving observer. ## The relative speed of a moving object in a certain direction differs according to the observer state and the direction of its movement as shown in the following table: | The observer state | Relative speed | Illustrating example | Static observer | | -------------------------- | ------------------------------------------------------------------------------------- | ------------------------------------------------- | ---------- | | 1. The observer is at rest | The relative speed = The real (actual) speed of the object. | The relative speed of the car = 100 km/h, | 100 km/h | | | | i.e "The relative speed is equal to the real speed". | | | 2. The observer is moving | The relative speed = The real speed of the object + The observer's speed. | The relative speed of the car = 100 + 60 = 160 km/h, | 100 km/h | | in the opposite direction | So, The real speed of the object = The relative speed of the object - The observer's speed. | i.e "The relative speed is more than the real speed". | | | of the moving object. | | | | | 3. The observer is moving | The relative speed = The real speed of the object - The observer's speed. | The relative speed of the car = 100-60 = 40 km/h, | 100 km/h | | in the same direction | So, The real speed of the object = The relative speed of the object + The observer's speed. | i.e "The relative speed is less than the real speed". | | | at different speed. | | | | | 4. The observer is moving | The relative speed = The difference between the two speeds = Zero. | The relative speed of the car = 60-60 = Zero. | 60 km/h | | in the same direction | | i.e. "The object seems static". | | | at the same speed. | | | | ## **G.R.** The moving car seems stable (at rest) to an observer moves at the same speed and the same direction. Because the relative speed equals the difference between their speeds equals zero. ## What is meant by ...? - The relative speed of a moving car is 90 km/h. This means that the speed of the car relative to an observer equals 90 km/h. - The relative speed of a moving object equals its real speed. This means that the observer is at rest. - The relative speed of a moving car equals 70 km/h to an observer moves in the opposite direction at a speed 20 km/h. This means that the real speed of the car equals 50 km/h. ## When the following happens...? - The relative speed of a moving object relative to an observer equals to double of its real speed. When the observer moves in the opposite direction at the same speed of the moving object. - The relative speed of a moving object relative to an observer equals to zero. When the observer moves in the same direction at the same speed of the moving object. ## We can summarize the previous explanation in the following diagram: The relative speed of a moving object in a certain direction is related to | **A static observer** | **A moving observer** | | ------------------------- | ----------------------- | | | in the same direction | | | in the opposite direction | | at the same speed | at the same speed | | at different speed | | | The relative speed | The relative speed | The relative speed | The relative speed | | = The real speed | = Zero | = The real speed | = The real speed | | | | + The observer's speed | # Problems ## 1 Calculate the actual speed of the car, whose relative speed is 50 km/h relative to an observer moving in the opposite direction at a speed of 30 km/h. ### Solution - Relative speed = Actual speed + Observer's speed - Actual speed = Relative speed - Observer's speed - Actual speed = 50 - 30 = 20 km/h. ## 2 A train (X) is moving at a speed of 90 km/h and another train (Y) is moving parallel to it at a speed of 60 km/h. What is the relative speed of the train (X) relative to: 1. An observer stands on the platform of the station. 2. An observer sits in the train (Y) if he is moving in: - (a) the same direction. - (b) the opposite direction. ### Solution 1. The relative speed of the train (X) relative to an observer standing on the platform = Its actual speed = 90 km/h. 2. The relative speed of the train (X) relative to an observer sitting in the train (Y) and moving in: - (a) the same direction = the difference between the two speeds = 90-60 = 30 km/h. - (b) the opposite direction = The sum of the two speeds = 90 + 60 = 150 km/h. ## Question? Two cars move in the same direction, car (A) moves at speed of 30 km/h and car (B) moves at speed of 80 km/h, while car (C) moves in the opposite direction at speed of 40 km/h. Calculate the relative speed of car (B) relative to an observer: 1. Stands on the ground. 2. In car (A). 3. In car (C). | **30 km/h** | **80 km/h** | **40 km/h** | **Static observer** | | ------------- | ----------- | ----------- | ---------------- | | A | B | C | | # Science, Technology and Society The time needed for the sunlight to reach the Earth is determined by the relation: speed of light = Distance / Time By knowing * The distance between the Earth and the Sun equals 149 million km (approximately). * The regular speed of the light in the space equals 300 000 km/sec. So, The time needed for the sunlight to reach the Earth (t) = d/V = 149 x 10^6 km / 300 000 = 497 sec. = 8 minutes and 17 seconds. | **The Sun** | **149 x 10^6 km** | **The Earth** | | ----------- | ----------------- | ----------- | i.e. If the time of sunrise is six o'clock. This means that the light travelled from the Sun at five o'clock and fifty one minutes and 43 sec. - 06:00:00 (The time of sunrise) - 00:08:17 (The time needed for the sunlight to reach the Earth) - 05:51:43 (The time at which the sunlight travelled from the Sun) ## **TRY** to answer worksheet 2 in the Notebook