Physics 10th Grade Quarter Test I PDF

Physics 10th Grade Physical Quantities & Measurement Techniques Contents Measurement Scalars & Vectors Calculating with Vectors Scalars & Vectors All quantities can be one of two types: A scalar ○ Scalar quantities have only a magnitude Mass is an example of a scala...

Physics 10th Grade Physical Quantities & Measurement Techniques Contents Measurement Scalars & Vectors Calculating with Vectors Scalars & Vectors All quantities can be one of two types: A scalar ○ Scalar quantities have only a magnitude Mass is an example of a scalar quantity because it has magnitude without direction Energy and volume are also examples of scalar quantities A vector ○ Vector quantities have both magnitude and direction Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction Acceleration and momentum are also examples of vector quantities Distance and Displacement Distance is a measure of how far an object has travelled, regardless of direction ○ Distance is the total length of the path taken ○ Distance, therefore, has a magnitude but no direction ○ So, distance is a scalar quantity Displacement is a measure of how far it is between two points in space, including the direction ○ Displacement is the length and direction of a straight line drawn from the starting point to the finishing point ○ Displacement, therefore, has a magnitude and a direction ○ So, displacement is a vector quantity Distance and Displacement (cont.) What is the difference between distance and displacement? When a student travels to school, there will probably be a difference between the distance they travel and their displacement The overall distance they travel includes the total lengths of all the roads, including any twists and turns The overall displacement of the student would be a straight line between their home and school, regardless of any obstacles, such as buildings, lakes or motorways, along the way Speed and velocity Speed is a measure of the distance travelled by an object per unit time, regardless of the direction ○ The speed of an object describes how fast it is moving, but not the direction it is travelling in ○ Speed, therefore, has magnitude but no direction ○ So, speed is a scalar quantity Velocity is a measure of the displacement of an object per unit time, including the direction ○ The velocity of an object describes how fast it is moving and which direction it is travelling in ○ An object can have a constant speed but a changing velocity if the object is changing direction ○ Velocity, therefore, has magnitude and direction ○ So, velocity is a vector quantity Motion in one direction Contents Speed & Velocity Acceleration Distance-Time Graphs Speed-Time Graphs Calculating Acceleration from Speed-Time Graphs Freefall Speed & velocity The speed of an object is defined as Distance travelled per unit time Speed is a scalar quantity ○ This is because it only contains a magnitude (without a direction) For objects that are moving at a constant speed, the equation for calculating speed is: S = d/t Where: ○ S = speed, measured in metres per second (m/s) ○ d = distance travelled, measured in metres (m) ○ t = time, measured in seconds (s) Average speed The speed of an object can vary throughout its journey Therefore, it is often more useful to know an object's average speed The equation for calculating the average speed of an object is: Average speed considers the total distance travelled and the total time taken Average speed (cont.) Velocity Velocity is a vector quantity with magnitude and direction Velocity is defined as: ○ Speed in a given direction The direction of a velocity can be given in words ○ For example, 20 m/s east Or the direction of velocity can be given using a positive or negative value ○ For example, −20 m/s A positive direction is typically in the direction of the initial motion, to the right, or upward A negative velocity is typically in the opposite direction to the initial velocity, to the left, or downward Velocity Vs. Speed Velocity The equation for velocity is very similar to the equation for speed: v = Δx / t Where: v = velocity in metres per second (m/s) Δx = displacement, measured in metres (m) t = time, measured in seconds (s) Velocity is a vector quantity, so it uses displacement, Δx, which is another vector quantity Worked Example 1 Find the displacement, average velocity, and average speed of the car in the Figure between positions A and F. Answer note that xA = - 30 m at tA = 0 s and that xF = -53 m at tF = 50 s. (a) Displacement (b) Average velocity (c) Average speed Worked Example 2 A teacher drives home from work travelling a total distance of 10.6 km. The journey takes 15 minutes. Calculate the teacher's average speed for the journey. Answer Step 1: List the known quantities Total distance (d) = 10.6 km, Total time (t) = 15 minutes Step 2: Convert the values to SI units 1 km = 1000 m, d = 10.6 × 1000 = 10 600 m 1 minute = 60 s, t = 15 × 60 = 900 s Step 3: Write out the average speed equation average speed= total distance travelled / total time taken Step 4: Substitute the known values to calculate average speed = 10 600 / 900 = 11.7 m/s Worked Example 3 A car travels north on a motorway with a velocity of 33 m / s. Determine the displacement of the car in 2 minutes. Answer Step 1: List the known quantities velocity, v = 33 m / s, time, t = 2 minutes Step 2: Convert the values to SI units 1 minute = 60 s, Therefore, 2 minutes = 2 × 60 = 120 s Step 3: Rearrange the velocity equation to make displacement to subject v = Δx / Δt ,, Multiply both sides by t, then put displacement on the left Δx = v Δt Step 4: Substitute in the known values to calculate Δx = 33 × 120 Δx = 3960 m north Worked Example 4 A helicopter flies the route shown in the figure It stops at point (I) for 30 min to pick up some cargo The total time the helicopter takes between taking off from H and landing at L is 4 hours. Calculate the average speed of the helicopter when it is flying Answer Average speed = total distance travelled / time in the air = 100 + 50 + 30 + 70 / (4 - 0.5) = 71.4 km / h Worked Example 5 During a training flight, a fight jet travelling at 300 m/s makes a turn to avoid bad weather Compare the speed and velocity between points A and B in the figure Answer (a) Compare the speed and velocity between points A and B on the diagram: Compare the speed at A and the speed at B: The speed is constant/the same at A and B OR the speed is 300 m/s at both points (b) Compare the velocity at A and the velocity at B: The velocity is different; The difference between speed and velocity is to do with direction ○ Since the directions are different, or the velocity points right at A and left at B, this means the velocities are different at points A and B Speed does not depend on the velocity, just the magnitude (size) Worked Example 6 During a Go Karting race, a car does 8 laps of a 300 m course. It takes 4.0 minutes to complete the race. What was the average speed of the Go Kart? A. 75 m/s B. 10 m/s C. 1.25 m/s D. 600 m/s Worked Example 7 Planes fly at typical average speeds of around 250 m/s. Calculate the distance travelled by a plane moving at this average speed for 2 hours. Answer Acceleration Acceleration describes how the velocity of an object changes over time Acceleration is defined as: The rate of change of velocity In other words, acceleration is the change in velocity per unit time The acceleration of an object is often changing throughout an object's journey Therefore, is it often useful to know the average acceleration Where: a = acceleration in metres per second squared (m/s ) ∆v = change in velocity in metres per second (m/s) ∆t = time taken in seconds (s) Illustrative Example A motorbike has an initial velocity of 0 m/s, and a final velocity of 5 m/s. It took 2.5 s to move from initial to final velocity. Calculate the acceleration. Acceleration (cont.) Acceleration (cont.) Speeding up & slowing down An object can change its velocity in several ways: ○ speeding up ○ slowing down ○ changing direction Any change in an object's velocity is an acceleration When an object speeds up, it is accelerating ○ This is positive acceleration When an object slows down, it is decelerating ○ This is negative acceleration Acceleration is positive if its direction is in the same direction as the motion of the object Acceleration (cont.) Worked Example 8 In the future, on unknown planet, an astronaut throws a ball upward with a speed of 2.5 m/s. 8.0 s later, the ball is travelling down to the floor with a speed of 4.3 m/s. Calculate the acceleration of the ball and give the direction of acceleration Answer Worked Example 9 A jet lands on an aircraft carrier at 63 m/s. What is its acceleration (assumed constant) if it stops in 2.0 s due to an arresting cable that snags the airplane and brings it to a stop? Answer Worked Example 10 A rocket is launched vertically upwards from the ground. The rocket travels with uniform acceleration from rest. After 8.0 s, the speed of the rocket is 120 m/s. Calculate the acceleration of the rocket. Answer Worked Example 11 The Figure shows the axes of a distance-time graph for an object moving in a straight line. Between time = 10 s and time = 20 s the object accelerates. The speed at time = 20 s is 9.0 m/s. Calculate the average acceleration between time = 10 s and time = 20 s. Answer Worked Example 12 A Japanese bullet train decelerates at a constant rate in a straight line. The velocity of the train decreases from 50 m/s to 42 m/s in 30 seconds. (a) Calculate the change in velocity of the train. (b) Calculate the deceleration of the train, and explain how your answer shows the train is slowing down. Answer Part (a) Step 1: List the known quantities Initial velocity, vi = 50 m/s Final velocity, vf = 42 m/s Step 2: Write the equation for change in velocity ∆v = vf − vi Step 3: Substitute values for final and initial velocity ∆v = 42− 50 ∆v = − 8 m/s Answer (cont.) Part (b) Step 1: List the known quantities Change in velocity, ∆v = − 8 m/s Time taken, ∆t = 30 s Step 2: Write the equation for acceleration Step 3: Substitute the values for change in velocity and time a = −8 / 30 a = − 0.27 m/s2 Step 4: Interpret the value for deceleration The answer is negative, which indicates the train is slowing down Motion with constant (uniform) acceleration Motion with constant (uniform) acceleration (cont.) This powerful expression enables us to determine an object’s velocity at any time t if we know the object’s initial velocity vi and its (constant) acceleration a. This equation provides the final position of the particle at time t in terms of the initial and final velocities. Motion with constant (uniform) acceleration (cont.) This equation provides the final position of the particle at time t in terms of the initial velocity and the acceleration. This equation provides the final velocity in terms of the acceleration and the displacement of the particle. Worked Example 13 A runner finishes a 100-meter dash in 8 seconds. Determine his average speed. Answer, Worked Example 14 A car can go from zero to 30 m/s in 2 seconds. Determine the car’s average acceleration. Answer, Worked Example 15 An aircraft starts from rest and accelerates on a straight runway at a rate of 8 m/s 2 for 400 meters. How much time does this take? Answer Given information Worked Example 16 A test car accelerates from rest at 4 m/s2 over the course of 200 m. How fast does the car go at the end of this acceleration? Answer Given information Worked Example 17 A car starts from rest and accelerates uniformly at 0.25 m/s2. How long will it take to cover 50 m. Answer Given Information Worked Example 18 An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s2 for 40.0 s. What is its final velocity? Worked Example 19 Blood is accelerated from rest to v = 30.0 m/s in a distance of 1.80 m by the left ventricle of the heart. Assume constant acceleration. (i) Find the acceleration a. (ii) For how long does the blood accelerate? Worked Example 20 Dragsters can achieve an average acceleration of 26.0 m/s². Suppose a dragster accelerates from rest at this rate for 5.56 sec. How far does it travel in this time? Worked Example 21 A car moves forward up a hill at 12 m/s with a uniform backward acceleration of 1.6 m/s². a. What is its displacement after 6.0 s? b. What is its displacement after 9.0 s? Worked Example 22 A jogger runs down a straight stretch of road with an average velocity of 4.00 m/s for 2.00 min. What is his final position, taking his initial position to be zero? Freely Falling objects (y-dimension) Acceleration of free fall In the absence of air resistance, all objects fall with the same acceleration regardless of their mass This is called the acceleration of freefall ○ This is also sometimes called acceleration due to gravity acceleration of freefall= g= 10 m/s2 Freely Falling objects Two common problems 1. Acceleration and velocity are always in the same direction a. No, as an object is thrown upward, velocity is +y, acceleration is –y 2. Acceleration is zero at the highest point. a. No, at the highest point, the velocity is zero, but acceleration is always -10 m/s2 b. The object changes velocity, it must have an acceleration Free Falling objects (cont.) Old Equations (Horizontal) New Equations (Vertical) Worked Example A construction worker accidentally drops a brick from a high scaffold. a. What is the velocity of the brick after 4.0 s? (40 m/s) b. How far does the brick fall during this time?(80 m) Worked Example A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above the ground. a. How high does the ball rise? (25.3 m) b. How long does the ball remain in the air? (4.5 s) Hint: The time it takes the ball to rise equals the time it takes to fall. Worked Example An object is thrown vertically upwards with an initial velocity of 20 m/s from the edge of a cliff that is 25 m from the sea below, as shown in the figure. Determine: (a) the ball's maximum height (20 m) (b) the time taken for the ball to reach its maximum height (2 s) (c) the time to hit the sea (5 s) (d) the speed with which it hits the sea (30 m/s) (You may approximate g to 10 m/s2)