Physics Answer Note #39

Question 1 A car travels with uniform motion from a position of 2 km North to a position of 20 km South in 0.50 hours. Solve: a. Displacement covered b. Velocity of the car c. Distance traveled by the car d. Speed of the car Answer a. Displacement covered: Displacement is the distance between the initial position and the final position of an object. In this case, the car moved from 2 km North to 20 km South, which means a total displacement of 22 km. However, displacement also includes direction, so the complete displacement of the car can be written as -22 km (South is considered negative direction). b. Velocity of the car: Velocity is the rate of change of displacement with respect to time. It can be calculated by dividing the displacement by the time taken. In this case, the displacement was -22 km and the time taken was 0.50 hours. Hence, the velocity of the car can be calculated as -22 km/0.50 hours = -44 km/h. c. Distance traveled by the car: Distance is the actual path traveled by an object and it is always a positive value. In this case, the distance traveled by the car can be calculated by adding the magnitudes of the initial and final positions, which is 2 km + 20 km = 22 km. d. Speed of the car: Speed is the rate of change of distance with respect to time. It is similar to velocity but does not include direction. The speed of the car can be calculated by dividing the distance traveled by the time taken. In this case, the speed can be calculated as 22 km/0.50 hours = 44 km/h. Question 2 The race director notices a Formula One racing car that has a velocity of 360 km/h NW. What displacement will the racing car make in 30 seconds before the race director checks its position again? Answer According to Newton's first law of motion, an object in motion will continue moving at a constant velocity unless acted upon by an external force. Therefore, we can use the formula d = vt to calculate the displacement (d) of the Formula One racing car in 30 seconds before the race director checks its position again. First, we need to convert the given velocity from km/h to m/s, since the formula requires the velocity to be in meters per second. To do this, we will divide 360 km/h by 3.6 to get 100 m/s. Next, we will plug in the values into the formula d = vt. We have the velocity (v) as 100 m/s and the time (t) as 30 seconds, therefore d = (100 m/s)(30 s) = 3000 m. Hence, the displacement of the Formula One racing car in 30 seconds before the race director checks its position again is 3000 meters in the northwest direction. Question 3 What is physics and how can we use it in our daily life and give an equation and explanation of how physics is shown and how it can be in our implemented in our daily life Answer Physics is a branch of science that deals with the study of matter, energy, motion, and the interactions between them. It is a fundamental science that helps us understand the laws and principles that govern the world around us. Physics is used in many aspects of our daily lives, from the technology we use to the natural phenomena we encounter. One way that physics is utilised in our daily life is through electricity. The flow of electric current through circuits is governed by the laws of physics, specifically Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This can be represented by the equation I = V/R, where I is the current in amps, V is the voltage in volts, and R is the resistance in ohms. This equation helps us understand and control the flow of electricity, which is essential in our daily use of electronic devices such as phones, computers, and appliances. Another application of physics in our daily life is through the use of magnetic fields. Magnets are used in everyday objects such as speakers, refrigerators, and credit cards, and their behavior can be described by the laws of electromagnetism. Ampere's Law, for example, explains the magnetic field created by a current-carrying wire and its surrounding magnetic flux. This equation, B = (μ0/4π)(I/r), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current in amperes, and r is the distance from the wire, helps us understand how electromagnets work and how we can use them in various devices. Furthermore, physics plays a crucial role in transportation. The laws of motion and mechanics, as described by Isaac Newton, helped engineers design and build cars, airplanes, and other forms of transportation. The equation F = ma, where F is the force acting on an object, m is its mass, and a is its acceleration, is a fundamental concept in physics that is essential in understanding the mechanisms behind transportation. In conclusion, physics is a vital science that has countless applications in our daily life. From electricity to magnets to transportation, the laws and principles of physics are at play, helping us understand and improve the world around us. By studying physics, we gain a deeper appreciation and understanding of our surroundings and how we can use it to our advantage. Question 4 a ball is thrown vertically upwards from the ground. The ball rises to a height of 10m and then falls and bounces. After each bounce it rises to 4/5 of the height of the previous bounce. Find the total distance that the ball travels from the first throw to the fifth impact with the ground. Answer To solve this problem, we will use the concept of geometric sequences. In this case, the height of the ball after each bounce forms a geometric sequence with a common ratio of 4/5. The first term of the sequence is the initial height of 10m. Therefore, we can create a formula to represent the height of the ball after each bounce: h(n) = 10 * (4/5)^n-1 Where n represents the number of bounces. To find the total distance traveled by the ball, we need to calculate the sum of the distances traveled during each interval between bounces. This can be done using the formula for the sum of a geometric sequence: Sn = a * (1-r^n) / (1-r) Where a represents the first term of the sequence, r represents the common ratio, and n represents the number of terms in the sequence. Since we are looking for the distance traveled from the first throw to the fifth impact, we will plug in n=5 into the above formula: S5 = 10 * (1 - (4/5)^5) / (1 - 4/5) S5 = 10 * (1 - (4/5)^5) / (1/5) S5 = 10 * (1 - (4/5)^5) * 5 S5 = 10 * (1 - 1024 / 3125) * 5 S5 = 10 * (2101 / 3125) * 5 S5 = 4202 / 625 S5 = 6.7232 m Therefore, the total distance traveled by the ball from the first throw to the fifth impact is approximately 6.72 meters. Question 5 The speed of a particle traveling along a straight line within a liquid is measured as a function of its position as v=(120−s) mm/s , where s is in millimeters.Determine the distance the particle travels before it stops. Answer To determine the distance the particle travels before it stops, we need to first understand the given equation. The equation v=(120−s) mm/s represents the velocity of the particle in millimeters per second as a function of its position s in millimeters. The variable "s" represents the distance of the particle from its initial position. To solve this problem, we can set the final velocity of the particle to 0, as the particle will stop moving when its velocity is 0. Therefore, we can write the equation as 0=(120-s) mm/s. Solving for s, we get s=120 mm. This means that the particle will travel a distance of 120 mm before it stops. We can also verify this by calculating the area under the velocity-time graph.