Kinematics PDF

Objectives 1. Explain the difference between scalar and vector quantities, providing examples of each. 2. Explain displacement and teach students how to calculate it using initial and final positions. 3. Difference between distance and displacement and their respective importanc...

Objectives 1. Explain the difference between scalar and vector quantities, providing examples of each. 2. Explain displacement and teach students how to calculate it using initial and final positions. 3. Difference between distance and displacement and their respective importance in studying motion. 4. Introduce the basic kinematic equations and their applications. 5. Interpreting displacement /time graphs and velocity / time graphs  Kinematics Kinematics is the branch of physics that deals with the analysis of the motion of objects without concern for the forces causing the Example of Motion Free fall objects Scalar and Vector Scalar -quantity with magnitude only Vector -quantity with both magnitude (size) and direction Examples Scalars: Distance Speed Time Mass Energy Vector: Displacement Velocity Acceleration Momentum Force Distance vs Displacement Scalar Vs Vector Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position  50KM 20KM Examples 1. 2.What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school? 3. What is the distance and the displacement of the race car drivers in the Indy 500? Distance and Displacement  Speed vs Velocity Speed (v) –how fast you go Average speed ( v) –distance/time (Scalar) Velocity (v) –how fast and which way; the rate at which position changes (Vector) Example While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Given: distance=440 miles Time = 8 hours Example 1 A car travels 300 metres north, then 400 metres south, all in 20 seconds. Calculate its average speed and its average velocity over this journey. Average Speed versus Instantaneous Speed Instantaneous Speed - the speed at any given instant in time. Average Speed - the average of all instantaneous speeds; found simply by a distance/time ratio. Example While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Given: distance=440 miles Time = 8 hours 1. Interpreting displacement /time graphs and velocity / time graphs Graphs-distance time graph position/time graph A- stationary B- constant velocity C- constant velocity returning to start D- acceleration E- deceleration F- constant velocity Gradient= speed Velocity vs time graph 1. Above is a velocity-time graph of a moving car. Answer the following questions using the graph. _____ a. At what time was the car stopped? _____ b. At what time did the car have the greatest velocity? _____ c. What was the greatest velocity? _____ d. At what time(s) was the car accelerating? _____ e. How fast was the car going at 1.0h? _____ f. What is the acceleration at 0.9 hr? 0 - 8 seconds: ___________ ____ from ____ metres per second to ____ metres per second. (Constant/uniform _____________ ). 8 - 11 seconds: __________ _________ of ____ metres per second. 11 - 18 seconds: ___________ _______ from ____ metres per second to ____ metres per second. (Constant/uniform ____________ ) Activity Given: Speed/Velocity, distance/ displacement, Acceleration 1. Calculate the speed for a car that went a distance of 125 kilometers in 2 hours time. 2. What is the speed of a cheetah that travels 112.0 meters in 4.0 seconds? 3. Calculate the average speed (in meters/sec) if a golf cart runs 140 meters in 10 seconds 4. Calculate the average speed (in Km/hr) of Charlie who runs to the store 4 Km away in 30 minutes? 5.. Calculate the distance (in Km) that Charlie runs if he maintains the average speed from question 2 for 1 hour 6. A bicycle rider travels 50.0 Km in 2.5 hours. What is the cyclist’s average speed? 5. What is the average speed (in miles per hour) of the car that traveled a total of 200 miles in 5.5 hours. 7. How much time would it take for the sound of thunder to travel 2000 meters if sound travels a speed of 330 meters per sec. 8. How much time would it take for an airplane to reach its destination if it tr5aveled at an average speed of 790 Km/hr for a distance of 5000 kilometers/ 9. An ant can travel approximately 30 meters per minute. How many meters could an ant move in 45 minutes? 10. If humans originated in Africa and migrated to other parts of the world, some time would be required for this to occur. At the modest rate of one kilometer per year, how many centuries would it take for humans originating in Africa to travel to China, some 10,000 Kilometers away? Acceleration: is the rate of change of velocity. CALCULATIONS 1. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration? 2. A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds? 3. A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the car’s average acceleration. Acceleration: is the rate of change of velocity. Final and Initial Velocity ( a=(v-u)/t ) Final Velocity v=u+at Initial Velocity If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s/s for 3 seconds, u=v-at what will its final velocity be? 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard’s average acceleration? 5. A runner covers the last straight stretch of a race in 4 s. During that time, he speeds up from 5 m/s to 9 m/s. What is the runner’s acceleration in this part of the race? 6. You are traveling in a car that is moving at a velocity of 20 m/s. Suddenly, a car 10 meters in front of you slams on it’s brakes. At that moment, you also slam on your brakes and slow to 5 m/s. Calculate the acceleration if it took 2 seconds to slow your car down. 7. A ball is dropped from the top of a building. After 2 seconds, it’s velocity is measured to be 19.6 m/s. Calculate the acceleration for the dropped ball. Part A of this graph has a positive gradient (upwards sloping), which tells us that the object is accelerating (the velocity is increasing). We can tell this because at the start of part A, the object’s velocity was 0 m/s and at the end of part A, the object’s velocity was 6 m/s. Part B of the velocity time graph is flat. This means that the object is travelling at a constant velocity of 6 m/s. Part C has a negative gradient (downwards sloping), which means that the object is decelerating. We can tell that this is the case because at the start of part C (9 seconds), the object was travelling at 6 m/s and at the end of part C (12 seconds), the object was travelling at 0 m/s (the object had stopped). Here are the rules for velocity time graphs: An upwards sloping line/ a positive gradient means that the object is accelerating A horizontal line means that the object is travelling at a constant velocity A downwards sloping line/ a negative gradient means that the object is decelerating A point that touches the x-axis means that the object is stationary