Slide 1 / 182 Slide 2 / 182 Algebra Based Physics Kinematics in One Dimension 2015-11-30 www.njctl.org Slide 3 / 182 Slide 4 / 182 Table of Contents: Kinematics · Motion in One Dimension Click on the topic to go to that section Motion in One Dimension · Average Speed · Position and Reference Frame · Displacement · Average Velocity · Instantaneous Velocity · Acceleration · Kinematics Equation 1 · Free Fall - Acceleration Due to Gravity · Kinematics Equation 2 · Kinematics Equation 3 Return to Table of · Mixed Kinematics Problems Contents https://www.njctl.org/video/?v=ARE0bLtRFVI · Graphing Slide 5 / 182 Slide 6 / 182 Distance Distance We all know what the distance between two objects is... As you can see from your efforts, it is impossible to define distance. So what is it? Distance is a fundamental part of nature. It is so fundamental that What is distance? it's impossible to define. Everyone knows what distance is, but no What is length? one can really say what it is. However, distances can be compared. ALSO - you can't use the words "distance" or "length" in your definition; that would be cheating.
Slide 7 / 182 Slide 8 / 182 Distance Distance We can compare the distance between two objects to the We'll be using meter as our standard for measuring distance. distance between two other objects. The symbol for distance is "d". For convenience, we create standard distances so that we can easily make comparisons... and tell someone else about them. And the unit for the meter is "m" We will be using the meter as our unit for measuring distance. It's just that it's been accepted as a universal standard, so everyone knows what it is. d = 0.2 m This doesn't define distance, but it allows us to work with it. Slide 9 / 182 Slide 10 / 182 Time Time Similarly, everyone knows what time is... Like distance, time is a fundamental aspect of nature. But try defining it; what is time? It is so fundamental that it's impossible to define. Everyone knows what time is, but no one can really say what it is... However, like distances, times can be compared. Remember you can't use the word "time" or an equivalent to the word "time", in your definition. Slide 11 / 182 Slide 12 / 182 Time Time We can say that in the time it took to run around the track, the We will be using the second as our standard for measuring time. second hand of my watch went around once...so my run took 60 seconds. When we compare the time between two events to the The symbol for time is "t" time between two other events, we are measuring time. The unit for a second is "s". This doesn't t = 10s define time, but it allows click here for a us to work "minute physics" on measuring time with it. and distance
Slide 13 / 182 Slide 14 / 182 Speed Speed The units of speed can be seen by substituting the units for distance and time into the equation Speed is defined as the distance traveled divided by the time it took to travel that distance. s = d t speed = distance time meters second s = d t m We read this unit as s "meters per second" Speed is not a fundamental aspect of nature, it is the ratio of two things that are. Slide 15 / 182 Slide 15 (Answer) / 182 1 A car travels at a constant speed of 10m/s. This 1 A car travels at a constant speed of 10m/s. This means the car: means the car: A increases its speed by 10m every second. A increases its speed by 10m every second. B decreases its speed by 10m every second. B decreases its speed by 10m every second. C moves with an acceleration of 10 meters every second. C moves with an acceleration of 10 meters every second. Answer D D moves 10 meters every second. D moves 10 meters every second. [This object is a pull tab] https://www.njctl.org/video/?v=7E8c3jVbN2w https://www.njctl.org/video/?v=7E8c3jVbN2w Slide 16 / 182 Slide 16 (Answer) / 182 2 A rabbit runs a distance of 60 meters in 20 s; 2 A rabbit runs a distance of 60 meters in 20 s; what is the speed of the rabbit? what is the speed of the rabbit? S = d/t Answer S = 60m/20s S = 3 m/s [This object is a pull tab] https://www.njctl.org/video/?v=XrtRbPudROU https://www.njctl.org/video/?v=XrtRbPudROU
Slide 17 / 182 Slide 17 (Answer) / 182 An airplane on a runway can cover 500 m in 10 s; An airplane on a runway can cover 500 m in 10 s; 3 3 what is the airplane's average speed? what is the airplane's average speed? s = d/t Answer s = (500m)/(10s) s = 50 m/s [This object is a pull tab] https://www.njctl.org/video/?v=OJNi1GsWnuI https://www.njctl.org/video/?v=OJNi1GsWnuI Slide 18 / 182 Slide 18 (Answer) / 182 A car travels at a speed of 40 m/s for 4.0 s; A car travels at a speed of 40 m/s for 4.0 s; 4 4 what is the distance traveled by the car? what is the distance traveled by the car? s = d/t Answer d = st d = (40m/s)(4s) d = 160m [This object is a pull tab] https://www.njctl.org/video/?v=CWvo93CQnNI https://www.njctl.org/video/?v=CWvo93CQnNI Slide 19 / 182 Slide 19 (Answer) / 182 5 You travel at a speed of 20m/s for 6.0s; what 5 You travel at a speed of 20m/s for 6.0s; what distance have you moved? distance have you moved? s = d/t Answer d = st d = (20m/s)(6s) d = 120m [This object is a pull tab] https://www.njctl.org/video/?v=mPMcjq1CNxA https://www.njctl.org/video/?v=mPMcjq1CNxA
Slide 20 / 182 Slide 20 (Answer) / 182 6 You travel at a constant speed of 20 m/s; how much 6 You travel at a constant speed of 20 m/s; how much time does it take you to travel a distance of 120m? time does it take you to travel a distance of 120m? s = d/t Answer t = d/s t = (120m)(20m/s) t = 6 s [This object is a pull tab] https://www.njctl.org/video/?v=_8JNZyQXze4 https://www.njctl.org/video/?v=_8JNZyQXze4 Slide 21 / 182 Slide 21 (Answer) / 182 7 You travel at a constant speed of 30m/s; how much 7 You travel at a constant speed of 30m/s; how much time does it take you to travel a distance of 150m? time does it take you to travel a distance of 150m? s = d/t Answer t = d/s t = 150m/30m/s t = 5 s [This object is a pull tab] https://www.njctl.org/video/?v=k7od93faZ3E https://www.njctl.org/video/?v=k7od93faZ3E Slide 22 / 182 Slide 23 / 182 Average Speed The speed we have been calculating is a constant speed over Average Speed a short period of time. Another name for this is instantaneous speed. If a trip has multiple parts, each part must be treated separately. In this case, we can calculate the average speed for a total trip. Determine the average speed by finding the total distance you traveled and dividing that by the total time it took you to travel that distance. Return to Table of Contents https://www.njctl.org/video/?v=Ry-IJYdAYhk
Slide 24 / 182 Slide 25 / 182 Distance and Time Intervals Average Speed & Non-Uniform Motion The following pattern of steps will help us to find the average In physics we use subscripts in order to avoid any confusion speed: with different distances and time intervals. Find the total distance d total = d 1 + d 2 + d 3 For example: if an object makes a multiple trip that has three parts we present them as d 1 , d 2 , d 3 and the corresponding time Find the total time t total = t 1 + t 2 + t 3 intervals t 1 , t 2 , t 3 . Use the average speed formula s avg = d total t total Slide 26 / 182 Slide 27 / 182 Average Speed - Example 1 Example 1 - Step 1 You ride your bike home from school Write the given information in the table below: by way of your friend’s house. It takes you 7 minutes (420 s) to travel You ride your bike home Segmen Distance Time Speed the 2500 m to his house. You spend t from school by way of your 10 minutes there, before traveling friend’s house. It takes you (m) (s) (m/s) 3500 m to your house in 9 minutes 7 minutes (420 s) to travel (540 s). What was your average I the 2500 m to his house. speed for this trip? You spend 10 minutes II (600 s) there, before III traveling 3500 m to your house in 9 minutes (540 s). To keep things clear, we Total What was your average can use a table (graphic /Avg. speed for this trip? organizer) to keep track of the information... Slide 28 / 182 Slide 29 / 182 Example 1 - Step 1 Example 1 - Step 1 Write the given information in the table below: Write the given information in the table below: You ride your bike home You ride your bike home Segmen Segmen Distance Time Speed Distance Time Speed from school by way of your from school by way of your t t friend’s house. It takes you friend’s house. It takes you (m) (s) (m/s) (m) (s) (m/s) 7 minutes (420 s) to travel 7 minutes (420 s) to travel 2500 I I 420 the 2500 m to his house. the 2500 m to his house. You spend 10 minutes You spend 10 minutes II II (600 s) there, before (600 s) there, before III III traveling 3500 m to your traveling 3500 m to your house in 9 minutes (540 s). house in 9 minutes (540 s). Total Total What was your average What was your average /Avg. /Avg. speed for this trip? speed for this trip?
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