Fundamentals of Kinematics

Capturing and displaying Motion: Nowadays we have the technology to capture sequences of fleeting (passing) instants and analyse the motion they reveal. High-speed flash photography can ‘freeze’ a moving object, and multi-flash or stroboscopic photography can show us multiple images as the object interfaced with a computer to measure an object’s position at different times, and so calculate its speed and acceleration. Displacement is distance moved in a particular direction. Speed is the rate at which distance is covered. Average speed = total distance covered / total time taken. Velocity is speed in a specific direction and is defined as the rate of change of displacement. Acceleration is the rate of change of velocity. Don’t confuse ‘s’ for distance or displacement with ‘s’ for seconds, the SI unit of time, or with speed, which is usually represented by ‘u’ or ‘v’. Information from the ‘Graphs of motion’: Velocity is equal to the gradient of a displacement-time graph. Acceleration is equal to the gradient of a velocity-time graph. How to solve problems: Write down: s, u v, a, t. Identify those values you know (beware of starting or finishing at rest- this merely means u = 0 or v=0 Convert to consistent units Identify the equation containing three known quantities and the unknown quantity you wish to calculate. Use proper sign convention Q1: A tap drips into a sink which is 40cm below the end of the tap. How long does it take each drop to fall? (Use g = 9.8 m s-2) Q2: A stone falls vertically for 2s and embeds itself 2 cm in soft mud. What is its average deceleration in the mud? A1: 0.29s A2: 9600 m s-2 Describing Motion A helicopter ascends at a constant speed of 5 m/s. How far does it rise in 5 seconds? An empty toy wagon reaches the bottom of a hill and rolls onto the level ground at a speed of 1.5 m/s. How long will it take the wagon to come to a stop if its acceleration is -0.6 m/s2? A diver jumps vertically with a velocity of 4.0 m/s from a platform and enters the water 1.9 seconds later. How high is the platform? A driver backs a car at a velocity of -2.3 m/s from a driveway onto a street. If the acceleration of the car is 0.8 m/s2, how far onto the street does the car move before it comes to a stop? Vectors A soccer player runs forward a distance of 4 m, reverses direction and runs a distance of3 m, and then reverses direction again andruns a distance of 8 m. What distance does the player run? What is his displacement? After takeoff, an air-traffic controller locates a small plane 12.0 km southeast of the airport. At this point, the plane turns 20.0°to the east of its original flight path and flies21.0 km. What is the magnitude of the plane’s displacement from the airport? The moving sidewalk at an airport has a speed of 0.9 m/s toward the departure gate. A man is walking toward the departure gate on the moving sidewalk at a speed of1.0 m/s relative to the sidewalk. What is the velocity of the man relative to a woman standing off the moving sidewalk? On a similar moving sidewalk moving in the opposite direction, a child walks toward the terminal at a speed of 0.4 m/s relative to the sidewalk. What is the velocity of the man relative to the child? A hiker starts by walking along a straight path. He then turns and walks 260.0 m west. If he finds he is located 360.0 m exactly north of his starting point, what was his displacement along the path? A hammer slides down a roof that makes a 40.0°angle with the horizontal. What are the magnitudes of the components of the hammer’s velocity at the edge of the roof if it is moving at a speed of 4.25 m/s? A Mathematical Model of Motion One day a rabbit challenged a skunk to a race. The following v-t graph shows the motion of a crazy rabbit during the race. If the rabbit crosses the finish line at 12.0 s, what average velocity did the skunk maintain to cross the finish line a moment before the rabbit? Look at the v-t graph of a remote-controlled toy car below. At t=0.0 s, the car is located at +10cm In which time interval or intervals does the car have a constant velocity? In which time interval or intervals does the car have constant positive acceleration? Kinematics-M.A.Mumeed. 00966507433412 Copy Right: M.A.Mumeed ,Physics Teacher, I.I.S.R-K.S.A.-Mobile: 0507433412 m Page 3