Physics Kinematics Equations: Solving Problems with Examples, Study notes of Physics

Download Physics Kinematics Equations: Solving Problems with Examples and more Study notes Physics in PDF only on Docsity! The Magic Chart Honors Physics Magic Chart Equations “Who Cares” Quantity vf = vi + a t x x = vi t + 1/2 a t2 vf x = ½ (vi + vf) t a vf 2 = vi 2 + 2a x t x = vft - 1/2 a t2 Vi Now try these on your own: 1. You throw an object upwards from the ground with a velocity of 20m/s and it is subject to a downward acceleration of 9.8 m/s2. How high does it go? Given Formula Set up Solution vi=20 m/s vf=0 m/s a=-9.8 m/s2 x=? vf2 = vi2 + 2a x (0 m/s)2= (20 m/s)2 + 2 (-9.8 m/s2) x x=20.4 meters 2. You throw an object upwards from the ground with a velocity of 20m/s and it is subject to a downward acceleration of -9.8 m/ s2. How much later does it momentarily coming to a stop? Given Formula Set up Solution vi=20 m/s vf=0 m/s a=-9.8 m/s2 t=? vf = vi + a t =(20 m/s) + -9.8 m/s2t t=2.04 s 3. You throw an object upwards from the ground with a velocity of 20m/s and it is subject to an downward acceleration of 9.8 m/ s2. How high is it after 2.0s? Given Formula Set up Solution vi=20 m/s a= -9.8 m/s2 t=2 s x=? vf2 = vi2 + 2a x =(20 m/s)2 + 2 (-9.8 m/s2)x =20.4 m THE “WHO CARES” QUANTITY tells you which equation to use. For example, suppose you know a, x, and vi but not v or t. If you are looking for t, then you don't care about v, so use the equatio whose “WHO CARES” quantity v. If, however, you need to find use the equation whose “WHO CARES” quantity is t. What about problems that act along a different axis? How does the context of the problem change Example 2 A car is at rest when it experiences an acceleration of 2.0m/s2 towards the north for 5.0s. How far will it travel during the time it accelerates? Take a second to write down the facts in the problem and then determine which equation you would use. Since we’re not told where the car starts, let’s just define its initial position as the origin for this problem, zero. In that case, the distance it travels will just be its position, x, at the end of the problem. Then, x0 = 0 x = ? vo = 0 t= 5.0s a = 2.0m/s2 x = vot + ½at2 Example 3 An object accelerates from rest. How long will it take for it to travel 40m if its acceleration is 4m/s2? Given Formula Set up Solution vi=0 m/s a= 4 m/s2 t=? x=40 m x = vi t + 1/2 a t2 40 m = ½ (4 m/s2)t =20 s Example 4 A plane must reach a speed of 36m/s in order to take off and its maximum acceleration is 3.0m/s2. How long a runway does it require? Given Formula Set up Solution vi=0 m/s vf=36 m/s a= 4 m/s2 x=? vf2 = vi2 + 2a x (36 m/s)2=2(4m/s2)x =162 m