PHYS 200 Kinematics PDF

8/29/2024 Kinematics Reading materials Knight, Jones and Field (2018) Chapter 2 “Motion in o...

8/29/2024 Kinematics Reading materials Knight, Jones and Field (2018) Chapter 2 “Motion in one dimension Giancoli (2013) Chapter 2 “Describing Motion: Kinematics in One Dimension” 1 8/29/2024 Add a footer 1 Learning outcomes At the end students should be able to 1. Define and analyze. i. position, displacement, ii. speed, velocity, iii. acceleration 2. distinguish between displacement and distance travelled. 3. distinguish between speed and velocity. 4. calculate distance, displacement, velocity, and acceleration, given initial and final positions, and the path between the two, initial and final times, initial and final velocities. 5. Identify from the shape of a speed-time graph when a body is i. at rest ii. moving with constant speed iii. moving with changing speed 6. list the conditions for uniform motion. 7. apply the equations of motion with constant acceleration to solve problems. 8. describe the term free fall. 9. describe projectile motion. 10. determine horizontal and vertical components of projectile motion. 11. determine range and maximum of a particle in projectile motion. 2 8/29/2024 2 1  8/29/2024 Kinematics Mechanics Kinematics Dynamics Galileo Galilei 1 Isaac Newton 2 1 Source: https://www.britannica.com/biography/Galileo-Galilei Accessed 24 Jan 2022 2 Source: https://www.britannica.com/biography/Isaac-Newton Accessed 17 August 20212 3 8/29/2024 3 Position and displacement ⸹ All measurements are made relative to a frame of reference. ⸹ In the diagram below, the frame of reference is the origin, that is zero. ⸹ Position of an object at any moment is given coordinate  horizontal (x axis)  vertical (y axis) ⸹ Displacement (∆𝑥) is the change in position of the object. ∆𝑥 = 𝑥 − 𝑥 𝑦 𝑎𝑥𝑖𝑠 Positive direction: + Negative direction: - -3 -2 -1 0 1 2 3 𝑥 𝑎𝑥𝑖𝑠 origin 0 4 8/29/2024 4 2  8/29/2024 Example ⸹ if the particle moves from 𝑥 = 5 𝑚 to 𝑥 = 9 𝑚 ,  then the displacement is +4 𝑚.  The positive result indicates that the motion is in the positive direction. ⸹ if, the particle moves from 𝑥 = 7 𝑚 to 𝑥 = 2 𝑚,  then displacement is −5 𝑚.  The negative result indicates that the motion is in the negative direction. ⸹ if, the particle moves from 𝑥 = 7 𝑚 to 𝑥 = 2 𝑚 and to 𝑥 = 7 𝑚,  then displacement is 0 𝑚.  The result indicates that there was no displacement. ⸹ The sign in front displacement (∆𝑥) is important. ⸹ Displacement gives direction; therefore, displacement is a vector quantity. 5 8/29/2024 5 Distance travelled ⸹ Distance travelled is the length of a path followed by a particle. ⸹ Distance is a scalar quantity. ⸹ if the particle moves from 𝑥 = 5 𝑚 to 𝑥 = 9 𝑚 ,  then the distance is 4 𝑚. ⸹ if, the particle moves from 𝑥 = 7 𝑚 to 𝑥 = 2 𝑚,  then distance is 5 𝑚. if, the particle moves from 𝑥 = 7 𝑚 to 𝑥 = 3 𝑚 and to 𝑥 = 7 𝑚,  then distance is 8 𝑚. 6 8/29/2024 6 3  8/29/2024 Speed Velocity Speed of an object in uniform motion 𝑆𝑝𝑒𝑒𝑑 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣 = = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 = is a vector quantity is a scalar quantity Unit meter per second (m/s) Unit meter per second (m/s) The magnitude can be zero, negative, or positive. The magnitude can never be negative or zero. gives the magnitude of the speed and its direction. measures only how fast an object moves. 7 8/29/2024 Add a footer 7 Acceleration ⸹ 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = = ⸹ acceleration is a vector ⸹ deceleration  is often used to indicate that an object is slowing down, that is the magnitude of the velocity is decreasing  does not mean that the acceleration is necessarily negative. ⸹ A particle is speeding up, if the particle has the same sign for velocity and acceleration. ⸹ Equally, a particle is slowing down, if the particle has opposite signs for the velocity and acceleration. ⸹ When the acceleration is constant, its average and instantaneous values are the same. 8 8/29/2024 8 4  8/29/2024 𝑥 (𝑘𝑚) 15 10 5 𝑡 𝑡𝑖𝑚𝑒 minute 0 0 10 20 30 40 50 60 70 80 -5 -10 -15 -20 9 -25 8/29/2024 9 𝑥 (𝑘𝑚) 15 10 Slope = {gradient} 5 𝑡 (𝑡𝑖𝑚𝑒) 0 0 10 20 30 40 50 60 70 80 -5 -10 -15 -20 -25 10 8/29/2024 10 5  8/29/2024 𝑥 >0 𝑥 0 Particle below the origin, 0 0 0 Particle above the origin, 0 𝑦