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# Physics 151 week two notes PHYC 151 001

UNM

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This 2 page Class Notes was uploaded by Breanab on Sunday January 31, 2016. The Class Notes belongs to PHYC 151 001 at University of New Mexico taught by Dr. Dave Cardimona in Winter 2016. Since its upload, it has received 24 views. For similar materials see General Physics in Physics 2 at University of New Mexico.

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Date Created: 01/31/16

Chapter 2: Motion in One Dimension 2.1 Describing Motion distance = scalar , displacement = vector = Δx (orΔy ) ‘trajectory’ When she goes Position vs time x vs t): slope = velocity backwards, the slope and velocity are negative. speed = scalar , velocity = vector v = Δx v = Δy x Δt y Δt 2.2 Uniform Motion constant velocity ! no speed-up or slow-down AND no change in direction!! € € Δx = v xt , or x – x0= v xt – t 0 , which we usually write as x = vxt , taking initial time and position to be 0. 2.3 Instantaneous Velocity How fast are you going at this instant. [This implies letting the time intervaΔt , go to zero – which leads tovx= dx/dt , the first derivative.] From now on, “ v ” will always mean instantaneous velocity. 2.4 Acceleration A changing velocity = an acceleration. a = Δv x x Δt Note that, since velocity is a vector, a change in velocity means either a change in magnitude OR direction (or, of course, both). Units of acceleration: m/s 2€ s = m/s/s = m/s EXAMPLE 2.6: Animal acceleration Lions, like most predators, are capable of very rapid starts. From rest, a lion can €ustain an acceleration of 9.5 m/s for up to a second. How much time does it take a lion to go from rest to a typical recreational runner’s speed of 10 mph (or 4.5 m/s)? We usually take acceleration to be positive when it is in the same direction as the velocity. A “deceleration” is a negative acceleration – opposite the direction of the velocity, and therefore slowing the object down. The book ALWAYS takes “to the right” or “up” to be ‘positive’. Therefore, for the book, if an object is moving to the left (‘negative’ direction) and it has a negative acceleration, the object will go faster! (Since in that case, both the velocity AND the acceleration are negative – and thus in the same direction.) Acceleration = slope of v vs tcurve – OR – ‘curvature’ of x vs tcurve: x BetweenAand B: - accel, + vel. BetweenAand B: + accel, decreasing. At B: - accel, zero vel. At B: zero accel ! constant velocity. Between B and C: - accel, - vel. Between B and C: - accel, increasing. At C: no accel, - vel. Between C and D: - accel, decreasing. Between C and D: + accel, - vel. 2.5 Motion with Constant Acceleration Five variables (x, v, 0 , t, a) lead to five equations: (we will again take the initial time and position to be 0) v =v +0 t ----------Use when you don’t care about position, x 1 2 x = v 0 + 2 a t -----Use when you don’t care about final velocity, v v −v = 0 a x -----Use when you don’t care about time, t € 1 € x = 2(v +v 0) t ---- Use when you don’t care about acceleration, a x = v t − 1 a t------Use when you don’t care about initial velocity, v € 2 0 € NOTE: for the uniform motion described earlier, we set acceleration to zero ( a = 0 ). € EXAMPLE 2.8: Coming to a stop As you drive in your car at 15 m/s (around 35 mph), you see a ball roll into the street ahead of you. You hit the brakes and stop as quickly as you can. You come to rest in 1.5 s. How far does your car travel as you are braking to a stop? 2.6 Solving One-Dimensional Motion Problems Write down what you are given and what you are asked for. That then tells you which variable “you don’t care about”, and that tells you which equation to use!! It’s as simple as that!! EXAMPLE 2.11: Kinematics of a rocket launch A Saturn V rocket is launched straight up with a net constant acceleration of 18 m/s .2 After 150 s, how fast is the rocket moving and how far has it traveled? EXAMPLE 2.12: Calculating the minimum length of a runway A fully loaded Boeing 747 with all engines at full thrust accelerates at 2.6 m/s . lts minimum takeoff speed is 70 m/s. How much time will the plane take to reach its takeoff speed? What minimum length of runway does the plane require for takeoff? 2.7 Free Fall v at “top” = 0 a at “top” =g down “Free fall” is ANY motion in which ONLY gravity is involved. In this case, you will ALWAYS be given acceleration ( g). Thus, you will never use the fourth equation above. a on way up a on way down =g down = gdown Aristotle vs. Galileo: initial speed time up falling objects (depend) vs (do not depend) on weight of object. = final speed = time down EXAMPLE 2.14: Analyzing a rock's fall EXAMPLE 2.16: Finding the height of a leap A heavy rock is dropped from rest at the top A springbok antelope goes into a crouch to perform of a cliff and falls 100 m before hitting the ground.a leap straight up. It extends its legs forcefully, How long does the rock take to fall to the ground, accelerating at 35 m/s for 0.7 m. It then leaves the and what is its velocity when it hits? ground and rises into the air. With what speed does it leave the ground, and how high does it go?

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