Unit 4 – Module 1 Uniform Accelerated Motion The Cheetah: A cat that is built for speed. Its strength and agility allow it to sustain a top speed of over 100 km/h. Such speeds can only be maintained for about ten seconds. Photo © Vol. 44 Photo Disk/Getty Uniform Acceleration in One Dimension: • Motion is along a straight line (horizontal, vertical or slanted). • Changes in motion result from a CONSTANT force producing uniform acceleration. Distance and Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: s = 20 m A B Distance s is a scalar quantity (no direction): Contains magnitude only and consists of a number and a unit. (20 m, 40 mi/h, 10 gal) Distance and Displacement Displacement is the straight-line separation of two points in a specified direction. D = 12 m, 20o A q B A vector quantity: Contains magnitude AND direction, a number, unit & angle. (12 m, 300; 8 km/h, N) Distance and Displacement • For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W. Net displacement D is from the origin to the final position: D = 4 m, W What is the distance traveled? 20 m !! D 8 m,E x = -4 x x = +8 12 m,W Definition of Speed •Speed is the distance traveled per unit of time (a scalar quantity). d = 20 m A Time t = 4 s B v= d t = 20 m 4s v = 5 m/s Not direction dependent! Definition of Velocity •Velocity is the displacement per unit of time. (A vector quantity.) s = 20 m A D=12 m 20o Time t = 4 s B D 12 m v t 4s v = 3 m/s at 200 N of E Direction required! Examples of Speed Orbit 2 x 104 m/s Light = 3 x 108 m/s Jets = 300 m/s Car = 25 m/s Speed Examples (Cont.) Runner = 10 m/s Glacier = 1 x 10-5 m/s Snail = 0.001 m/s Acceleration •Acceleration is a measure of how fast velocity changes. Acceleration is the change of velocity divided by the change of time. Acceleration is a vector, and therefore includes both a size and a direction. Example of Acceleration •An object was moving north at 10 meters per second. The object speeds up and now is moving north at 15 meters per second. The object has accelerated. •Jane is walking east at 3 kilometers per hour. Jane's velocity does not change. Jane's acceleration is zero. Review of Symbols and Units •Displacement (x, xo); meters (m) •Velocity (v, vo); meters per second (m/s) •Acceleration (a); meters per s2 (m/s2) •Time (t); seconds (s) Review sign convention for each symbol Uniformly Accelerated Motion •A body has a uniformly accelerated motion if it travels in a straight line and its velocity increases by equal amounts in equal interval of time Formulas • A. • B. 𝑣𝑓= 𝑣𝑖 + 𝑎𝑡 𝑣𝑎𝑣𝑒= 𝑣𝑓+𝑣𝑖 2 • C. • D. 𝑎= 𝑣𝑓−𝑣𝑖 𝑡 d= (𝑣𝑓+𝑣𝑖) 𝑡 2 • E. d= 𝑣𝑖𝑡 + 0.5𝑎𝑡2 • F 𝑣𝑓2 = 𝑣𝑖2 + 2ad Sample Problem no. 1 •The brakes of a car provides an acceleration of -5.0 m/s2. How long will it take for a car travelling at 20. 0 m/s to stop? Sample Problem no. 2 •A truck starts from rest and accelerates at 2.0 m/s2 for 4.0 s. How far will it go at the end of this time? Answer this: •An airplane from rest accelerates on a runway at 5.50 m/s2 for 20.25 s until it finally takes off the ground. What is the distance covered before takeoff? Answer this! •A jeepney from rest accelerates from uniformly over a time of 3.25 seconds and covers a distance of 15 m. Determine the acceleration of the jeepney. Answer this! • A car covers 200.0 m while increasing its velocity from 20.0 m/s to 30.0 m/s. Compute for acceleration Answer this! •Starting from rest, a car accelerates at 2.0 m/s2. How far will it go after 6.0 s? Answer this! •A train accelerates to a speed of 20 m/s over a distance of 150 m. Determine the acceleration (assume uniform) of the train.