Practice Problem How long will it take a car going from 10 m/s to 50 m/s if the acceleration is 4 m/s2?
Practice Problem If a car slams on its breaks and comes to a complete stop, after driving for 20 seconds, what is its initial velocity if it were decelerating at -1.5 m/s2?
Speed and Acceleration Measuring motion
Measuring Distance Meter international unit for measuring distance. 1 mm = 50 m
Calculating Speed Speed (S) = distance traveled (d) / the amount of time it took (t). S = d/t
Units for speed Depends, but will always be a distance unit / a time unit l Ex. Cars: mi./h l Jets: km/h l Snails: cm/s l Falling objects: m/s
Calculating speed S = d/t If I travel 100 kilometer in one hour then I have a speed of 100 km/h If I travel 1 meter in 1 second then I have a speed of. 1 m/s
Average speed Speed is usually NOT CONSTANT l Ex. Cars stop and go regularly l Runners go slower uphill than downhill Average speed = total distance traveled/total time it took.
Calculating Average Speed It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets. Total Distance: l 40 km + 20 km = 60 km Total Time: l 1 h + 2 h = 3 hr Ave. Speed: l total d/total t = 60 km/3 h = 20 km/h Total _ Dist. Ave. _ Speed = Total _ time
Question I travelled 25 km in 10 minutes. How many meters have I travelled? l A) 25000 m l B).0112 m l C).025 m l D) 2.5 m 25 km * 1000m/km = 25000 m
Question I ran 1000 m in 3 minutes. Then ran another 1000 m uphill in 7 minutes. What is my average speed? Total ldist. A) 100 = 1000 m/min m + 1000 m = 2000 m l B) 2000 m/min Total ltime C) 10 = m/min 3 min + 7 min = 10 min l D) 200 m/min Ave speed = total dist/total time = l E) 20 m/min 2000m/10 min = 200 m/min = D
Velocity Velocity the SPEED and DIRECTION of an object. l Example: An airplane moving North at 500 mph A missile moving towards you at 200 m/s
Question What is the difference between speed and velocity? Speed is just distance/time. Velocity includes direction as well.
Graphing Speed: Distance vs. Time Graphs Denver Phoenix
Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise
Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise=? 600 km 3 h
Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise=? 600 m 3 minutes Rise/
Different Slopes Distance (km) 8 7 6 5 4 3 2 1 0 Slope = Rise/Run = 1 km/1 hr = 1 km/hr Run = 1 hr Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 1 km Run = 1 hr Rise = 0 km 1 2 3 4 5 6 7 Time (hr) Run = 1 hr Rise = 2 km Slope = Rise/Run = 2 km/1 hr = 2 km/hr
Question Average Speed Below = is Total a distance distance/total vs. time time graph = 12 of km/6 hr my position = during 2 km/hr a race. What was my AVERAGE speed for the entire race? Distance (km) 14 12 10 8 6 4 2 0 0 1 2 3 4 5 6 Run Time = (hr) 6 hr Rise = 12 km
Question What does the slope of a distance vs. time graph show you about the motion of an object? It tells you the SPEED
Question Below is a distance vs. time graph for 3 runners. Who is the fastest? 7 6 Distance (mi.) 5 4 3 2 1 0 0 1 2 3 4 5 6 35 Time (h) Bob Jane Leroy Leroy is the fastest. He completed the race in 3 hours
Acceleration Acceleration = speeding up Acceleration the rate at which velocity changes l Can be an: Increase in speed Decrease in speed Change in direction
Types of acceleration Increasing speed l Example: Car speeds up at green light Decreasing speed l Example: Car slows down at stop light Changing Direction screeeeech l Example: Car takes turn (can be at constant speed)
Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating
Calculating Acceleration If an object is moving in a straight line Acceleration = Final _ speed - Initial Time _ Speed Units of acceleration: l m/s 2
Calculating Acceleration Acceleration = Final _ Speed - Initial Time _ Speed = 16m / s - 4s 0m / s = 4m / s 2 0 s 1 s 2 s 3 s 4 s 0 m/s 4 m/s 8 m/s 12 m/s 16 m/s
Question A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver s average acceleration? Final _ speed - Initial Accel = Time 40m = = 10m / / s - 20m 2s s 2 / s = 20m 2s / s _ speed
Graphing Acceleration Can use 2 kinds of graphs l Speed vs. time l Distance vs. time
Graphing Acceleration: Speed vs. Time Graphs Speed (m/s) 14 12 10 8 6 4 2 0 0 1 2 3 4 5 6 Time (s) 1)Speed is increasing with time = accelerating 2)Line is straight = acceleration is constant
Graphing Acceleration: Speed vs. Time Graphs Speed (m/s) 14 12 10 8 6 4 2 0 Rise = 4 m/s Run = 2 s 0 1 2 3 4 5 6 Time (s) 1)In Speed vs. Time graphs: Acceleration = Rise/Run = 4 m/s 2 s = 2 m/s 2
Graphing Acceleration: Distance vs. Time Graphs Distance (m) 35 30 25 20 15 10 5 0 0 1 2 3 4 5 Time (s) 1)On Distance vs. Time graphs a curved line means the object is accelerating. 2)Curved line also means your speed is increasing. Remember slope = speed.
Question Speed (m/s) 14 12 10 8 6 4 2 0 Run = 3 s Rise = -6 m/s 0 1 2 3 4 5 6 Time (s) Above is a graph showing the speed of a car over time. 1) How is the speed of the car changing (speeding up, Slowing down, or staying the same)? 2) What is this car s acceleration? 1) The car is slowing down 2) Acceleration = rise/run = -6m/s 3s = -2 m/s 2
Question: Distance (m) 35 30 25 20 15 10 5 0 0 1 2 3 4 5 The black and red lines represent Time (s) a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down 1)Which line represents an object that is accelerating? Remember: in distance vs. time graphs: curved line = accelerating, flat line = constant speed
Question: Hard one Distance (m) Speed (m/s) 45 14 4012 35 10 30 258 206 15 4 10 52 0 0 1 22 3 3 4 4 5 5 6 6 Time (s) (s) Above is a graph showing the speed of a car over time. 1)What would a distance vs. time graph for this look like?
Acceleration A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster?
Acceleration A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0 m/s 2?
Acceleration If a car can go from 0 to 30 m/s in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting speed were 20 m/s?
Acceleration A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s 2. If the cart has a beginning speed of 2.0 m/s, what is its final speed?