Using Units in Science 5 cm x 2 cm=?10 cm 2 2 cm 2 1 How much is 150 miles divided by 3 hours? 150 miles/hr 50 miles 50 hrs 50 hrs/mile E 50 miles/hr 3 pears per orange 2 You buy 10 gallons of gas and you pay $25 for the gas. Which of the following is true? You pay $3 per gal You pay $0.33 per gal You get 3 gal per dollar You get 0.33 gal per dollar Some lgebra 2= 10 5 2= 10 5 a= b c a= b c Everything in the Universe is in motion, so in this chapter we learn how to describe the motion of objects-both on Earth and also in the heavens. Speed Speed is defined as the distance traveled divided by the time it took to travel that distance. speed = distance / time s = d/t Speed is not fundamental aspects of nature, it's the ratio of two things that are.
Speed The units of speed can be seen by substituting the units for distance and time into the equation for speed: s = d/t \ Speed meters / second Or m/s If you dri is v=100 mi/2hrs=? If you dri Pull Story 1.2 km distance 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 0 1 2 3 4 5 6 You stroll to a ice cream stand 1.2 km away from your house, walking at a steady pace you arrive in 20 minutes. It takes 5 minutes to eat you ice cream and then you head back at same speed. Halfway home you pause for 5 minutes to watch construction. You arrive 50 minutes after you left. How far did you walk? (distance) Velocity = isplacement (Final position- Initial Position) Time How fast did you walk? (speed) What was you average speed for the entire trip? (average speed) What overall change in your position occurred in the entire trip? (displacement) 1. Prepare a data table showing numbers to be plotted graph Look at the trip 2. Label horizontal and vertical axis with the same heading used in the data table. 3. hoose an appropriate scale unit and place numbers along axis so that all the numbers in the data table will fit. 4. Graph or plot the numbers Position (km) 1.4 1.2 1 0.8 0.6 5. raw a graph or smooth curve 0.4 0.2 Position (km) Time (minutes) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0 10 20 30 40 Time (min) 50-5
motion.m4v Pull Pull 3 You travel 60 meters in 20 s; Your average speed is m/s? 4 The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour 30 km in 2 hours 60 km in 1/2 hour 60 km in 2 hours 5 You travel at a speed of 40 m/s for 4.0 s; what distance have you moved? 6 You travel at a constant speed of 20 m/s; how much time does it take you to go a distance of 120m?
Speed is Relative When sitting on a chair, your speed is zero relative to the Earth but 30 km/s relative to the Sun. 20 km/h = 12 mi/h = 6 m/s 40 km/h = 25 mi/h = 11 m/s Velocity=Speed + irection e.g 50 km/hr=speed 50 km/hr North=velocity The car on the circular track may have a constant speed, but its velocity is changing every instant 3.htm isplacement is how far you are from where you started, regardless of how you got there. For instance, if you drive 600 miles to Ohio and then... isplacement -x +y -y +x The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. o both cars have the same speed? o they have the same velocity? isplacement is how far you are from where you started, regardless of how you got there. isplacement -x +y For instance, if you drive 600 miles to Ohio and then 200 miles back towards your home... For instance, if you drive 600 miles to Ohio and then 200 -x -y +x isplacement is how far you are from where you started, regardless of how you got there. miles back towards your home: You travel a distance of 800 miles, but your displacement is 400 miles, since that's how far you are from your home. isplacement +y -y +x
isplacement Now that we have the idea of position, we can talk about a change in position; a displacement. isplacement istance can only be positive since you can't travel a negative distance, but displacement can be positive or negative since you can end up to the right or left of where you started. +y +y The symbol for "change" is the Greek letter "delta" "Δ". So "Δx" means the change in x or the change in position -x x o xf +x -x xf x o +x displacement is a vector -y isplacement is positive. -y isplacement is negative. 7 You travel 60 m to the right and then 30 m to the left. What distance have you traveled? 8 You travel 60 m to the right and then 30 m to the left. What is your displacement? verage Velocity Speed is defined as the ratio of distance and time 9 You run completely around a 400m track. t the end of your run, what total distance have you traveled? s = d t Similarly, velocity is defined as the ratio of displacement and time Δx v = Δt
You run completely around a 10 400 m track. t the end of your run, what is your total displacement? Vectors and Scalars Vector - a vector is a quantity that has both a magnitude (number or value) and a direction Scalar - a scalar has only a magnitude Quantity Vector? Scalar? Time istance isplacement Speed 11 Velocity is a vector. True False If your speed is changing we say that you are accelerating. Suppose you are told that your driver will change speed from 50 mph to 70 mph. Is this a very large acceleration? acceleration = change of velocity elapsed time a = Δv Δt Suppose we are driving and in 1 second we steadily increase our velocity from 30 kilometers per hour to 35 kilometers per hour, and then to 40 kilometers per hour in the next second, to 45 in the next second, and so on. We change our velocity by 5 kilometers per hour each second. This change of velocity is what we mean by cceleration cceleration is a vector, although in one-dimensional motion we only need the sign. Since only constant acceleration will be considered in this course, there is no need to differentiate between average and instantaneous acceleration. Units for acceleration You can derive the units by substituting the correct units into the right hand side of these equations. a = Δv Δt m/s s = m/s 2
cceleration applies to decreases as well as increases and also curved paths You go from rest to 90 km/hr in 10 s. What is your acceleration? In 2.5 s a car goes fro 60 km/hr to 65 km/hr while a bike goes from rest to 5 km/hr in same time. Which undergoes a bigger acceration? 12 n automobile is accelerating when it is slowing down to a stop rounding a curve at a steady speed oth of the above Neither of the above 13 cceleration and velocity are actually the same rates but for different quantities the same when direction is not a factor the same when an object is freely falling 14 Your velocity changes from 60 m/s to the right to 100 m/s to the right in 20 s; what is your average acceleration? a = Δv Δt Pull 15 When a ball increases in speed by the same amount each second, its acceleration 16 If a ball rolls down an inclined plane and picks up 4 m/s each second it rolls, its acceleration is a. also increases each second. a. one-half of 4 m/s. b. decreases each second. b. one-half of 4 m/s 2. c. is constant. c. 4 m/s 2. d. fluctuates. d. 10 m/s 2.
17 The acceleration of a raindrop that falls at constant velocity a.is zero. b.is directed downward. c. decreases over time. d.increases over time. heck Yourself particular car can go from rest to 90 km/h in 10 s. What is its acceleration? 2. In 2.5 s a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the greater acceleration? What is the acceleration of each vehicle? 3.. What is the acceleration of a race car that whizzes past you at a constant velocity of 400 km/h? 4. Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 seconds or a skateboard that goes from zero to 5 km/h in 1 second? 18 glance at your speedometer will tell you your a.average speed. Suppose starting from rest you accelerate at 2 m/s/s (2 m/s 2 ). How fast will you be going in 1s? 2s? 3s? b.instantaneous speed. c. overall speed. d.acceleration. velocity= accleration x time
Gravity and Falling Objects hammer.mov freefallexpt.m4v feater.mov position galileofalling.mov contradiction.mov
Galileo and Free Fall Galileo found that a ball rolling down an inclined plane will pick up the same amount of speed in successive seconds; that is, the ball will roll with unchanging acceleration velocity= accleration x time Pull 19 free-falling object has a speed of 30 m/s at one instant. Exactly 1 s later its speed will be the same 35 m/s more than 35 m/s 60 m/s Galileo and falling odies Time Total istance 0 1 2 3 d ~ t 2 Galileo and falling odies Free Fall a= g ~ 10 m/s per sec Time Total istance 0 1 2 0 1 4 9 3 d ~ t 2 d (meters) ~ 5 t 2 ll objects moving under the influence of only gravity are said to be in free fall ll objects falling near the earth s surface fall with a constant acceleration Galileo originated our present ideas about free fall from his inclined planes The acceleration is called the acceleration due to gravity, and indicated by g
cceleration due to Gravity 20 uring each second of free fall, the speed of an object Symbolized by g a. increases by the same amount. g = 9.8 m/s 2 (We will occasionally use 10 m/s 2 ) g is always directed downward toward the center of the earth b. changes by increasing amounts each second. c. remains constant. d. doubles each second. Free Fall How Far? V avg = V 1 + V 2 2 d=vavgt= (v0+vf) 2 t = v f t 2 =at t 2 21 What is the distance covered of a freely falling object starting from rest after 4 s? 4 m d=½ gt 2 16 m 40 m 80 m d=½ gt 2
More lgebra: What is t? What is your reaction time? 200 = 2 t 2 200=5t 2 d=½ gt 2 heck Yourself cat steps off a ledge and drops to the ground in 1/2 second.1.what is its speed on striking the ground? 2.What is its average speed during the 1/2 second? 3.How high is the ledge from the ground? 22 cat steps off a ledge and drops to the ground in 1/2 second.1.what is its speed on striking the ground? 2.5 m/s 5 m/s 10 m/s 20 m/s 23 What is its average speed during the 1/2 second? 24 How high is the ledge from the ground? 2.5 m/s 0.5 m 5 m/s 1 m 10 m/s 1.25 m 20 m/s 2 m
t the end of 1 second of free fall, an apple falling from rest has a speed of n object in free fall has a speed of 60 m/s. One second later its speed is a. 1 m/s. b. 5 m/s. c. 10 m/s. d. more than 10 m/s. a. 10 m/s. b. 30 m/s. c. 60 m/s. d. 70 m/s. uring the upward part of this motion, the object slows as it rises. It should come as no surprise that it slows at the rate of 10 meters per second each second the same acceleration it experiences on the way down. So as Figure 3.8 shows, the instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward. The velocities are opposite, of course, because they are in opposite directions. Note that the downward velocities have a negative sign, indicating the downward direction (it is customary to call up positive, and down negative.) Whether moving upward or downward, the acceleration is 10 m/s 2 the whole time. 25 The speed of a vertically thrown ball at the top of its path is 0. 10 m/s 2. between 0 and 10 m/s 2. dependent on the mass of the ball. 26 The acceleration of a vertically thrown ball at the top of it's path is m/s 2 and halfway up is m/s 2. 0,0 10,0 10,0 10,10
27 n object is thrown straight up with an initial velocity of 40 m/s. How long to get to highest point? (assume g=10 m/s/s) E 2 sec 3 sec 4 sec 5 sec 10 sec 28 n object is thrown straight up with an initial velocity of 40 m/s. How high does it go? E 20 m 30 m 40 m 80 m 100 m d= v avg t= (0+40)/2 x 4 =80 m or d=1/2 gt 2 = 1/2 (10)(4) 2 = 80 m 29 n object is thrown straight up with an initial velocity of 40 m/s. The total time the ball is in the air is sec Summary Speed How fast something moves. The distance traveled per unit of time Velocity The speed of an object and specification of its direction of motion cceleration The rate at which velocity changes with time; the change in velocity may be in magnitude or direction or both Free fall Motion under the influence of gravity only. 03_FreeFallHowFar_VI.mov
30 Which of the following is not a vector quantity? velocity speed acceleration all are vector quantities