Velocity, Speed, and Acceleration Unit 1: Kinematics
Speed vs Velocity Speed is a precise measurement of how fast you are going. It is your distance traveled over time. Speed is a scalar quantity. To measure speed, you need to know two things: 1) Distance 2) Time Velocity is speed with a specific direction it is a vector quantity. To measure velocity you need to know three things: 1) Distance 2) Time 3) Direction
The skier has traveled 400 meters in 6 seconds. What is his speed? Distance traveled is 400 meters The time it took was 6 seconds. The speed is the distance traveled divided by the time taken. speed = 400 meters 6 seconds speed = 66.67 m s
Formula In this formula; x is the symbol for displacement Usually measured in meters t is the symbol for time The formula for velocity is v = x t Usually measured in seconds v is the symbol for velocity Usually measured in m/s. It must agree with whatever the distance and time is measured in! Velocity is actually speed with a direction (known as a VECTOR quantity). EX: 60 mph on I-80 going east.
Formula In this formula; d total is the symbol for total distance Usually measured in meters t total is the symbol for total time The formula for average speed is s avg = d total t total Usually measured in seconds s avg is the symbol for average speed Usually measured in m/s. It must agree with whatever the distance and time is measured in!
Problems When Evelyn Ashford was in the Olympics she broke the record for the 200 m run by completing it in 11s. What was her speed? Remember: We have a specific 5-step method for solving problems the GUESS method.
G: givens d = 200 m t = 11 s U: unknowns v =? E: equation v = x t S: substitution v = 200 11 S: solution v = 18 m/s G: write down the givens you can do any necessary conversions at this point. U: write down the unknowns E: write down the equation(s) you may want to re-arrange the equation at this point S: write down the substitution Plug everything in S: write down the solution remember to include the units! When Evelyn Ashford was in the Olympics she broke the record for the 200 m run by completing it in 11s. What was her speed?
Problems On average, a cheetah can reach speeds of up to 95 km/hr. If the cheetah can maintain that speed for about 30 seconds, how far will it travel in that time? G: givens v = 95 km/hr t = 30 seconds U: unknowns x =? E: equation 1 hour = 3600 seconds v = x t Rearrange for x, x = vt S: substitution x = ( 26.39 m/s)(30 sec) S: solution v = 791.7 m
Problems In 1931, "'Big Bill' Tilden delivered the fastest serve ever officially measured. The speed was 73.14 m/s. If the serve covered 30.5 m, how much time did Bill s opponent have to react before the ball reached him? G: givens x = 30.5 m v = 73.14 m/s U: unknowns t =? E: equation t = x v S: substitution t = 30.5m 73.14m/s S: solution t = 0.42 sec
ACCELERATION What is acceleration? The rate at which velocity changes compared to the time it takes to change. This is also a vector quantity because it includes a direction. a = v t = v f v i t = final velocity initial velocity change in time UNITS: m/s s = m/s/s or m/s 2
EX: If your old Chevy can go from 20 m/s to 60 m/s in 4 seconds, What is your car s acceleration? 1. Given: Initial Velocity = 20 m/s Final Velocity = 60 m/s Δ v = 60 20 = 40 m/s Time = 4 seconds 2. Unknown: 3. Equation: Acceleration =? a = v t 4 sec 4 sec 4. Substitute: 5. Solve: a = 40 4 a = 10 m/s 2 This means your car accelerates 10 m/s each second
More about acceleration. Lets say the stop light turns red and you put the brakes on. Are you accelerating? *Any change in speed, is acceleration. *Any change in direction is acceleration.
When is there zero acceleration? If you are traveling at a constant speed of 50 mph for 1 hour, are you accelerating? Remember: a = v t Is your speed changing? No? Then acceleration = 50 mph 50 mph = 0 mph = ZERO! 1 hr 1 hr *Acceleration is ZERO if you travel at a constant speed!* Zero acceleration = cruise control
All of the Kinematics Equations Based on what information you have, pick the correct equation!
Acceleration Practice You try the following problems 1. A car must come to an emergency stop. What is its acceleration if it took 8 seconds for it to stop when it was traveling at 30 m/s? 2. It was once recorded that a Jaguar left skid marks that were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s 2, determine the speed of the Jaguar before it began to skid.
Gravity pulls all things down toward the center of Earth with the same acceleration If you drop an object straight down and no other forces are acting on it, it accelerates in free fall. GRAVITY Free Fall Acceleration on Earth = - 9.8 m/s 2 (also known as the acceleration of gravity)
Gravity Problem A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well.
Visualizing Motion: Position and Time
Position vs. Time Graphs Distance/position runs vertically (the y-axis). The higher up the graph we go the further we are from the starting point Time always runs horizontally (the x- axis). The further to the right, the longer time that has passed since leaving the starting position The slope of a position time graph = change in position change in time Which is the equation for.??? VELOCITY!!!
P-T Graphs If something is not moving, a horizontal line is drawn on a distance-time graph. Time is increasing to the right, but its distance does not change. This graph shows an object that is stationary. Slope = 0 = velocity
P-T Graphs If something is moving at a steady speed, it means we expect the same increase in distance in a given time. Time is increasing to the right, and distance is increasing steadily with time. This graph shows an object that moves at a steady, constant speed.
P-T Graphs Both the lines below show that each object moved the same distance, but the steeper yellow line got there before the other one. What does this indicate? A steeper slope indicates a larger distance moved in a given time. In other words, higher speed. This is shown in yellow.
P-T Graphs For the first part of the journey shown by the graph below, the object moved at a constant (slow) speed. Then the object suddenly increased its speed, covering a much larger distance in the same time. The speed increased in the second part of the journey.
P-T Graphs There are three parts to the journey shown here Where is the graph showing motion that is: Stopped? B! C Moving at a quick constant speed? C! A B Traveling at a slow constant speed? A!
P-T Graphs: Negative Slopes What do these graphs, with a NEGATIVE SLOPE mean? They show an object that is moving leftward or backwards. C Negative in physics means left, down, West, or South Positive means right, up, North, or East
You Try It: Graphing Position Vs. Time Suppose you are helping a friend who is training for a track meet. She wants to know if she is running at constant speed. You mark the track in 50-meter increments and measure her time at each position during a practice run. Calculate her average speed based on the data. Time (s) Position (m) 0 0 10 50 20 100 30 150 s avg = d total = 150 t total 30 = 50 m/s
Graphing Position Vs. Time What is different about the data shown here? It s not changing at a constant rate. What does that mean? It means that she s accelerating and getting faster and faster in the same amount of time. Time (s) Position (m) 0 0 10 50 20 150 30 300
Position Vs. Time - Changing Velocity Now consider a car that has a changing velocity. It is not moving at a constant rate, but getting faster by the second (i.e. it s accelerating) What would this graph look like? You try it in your notes first
P-T Graphs: Acceleration The line below is curving upwards. This shows an increase in speed, since the slope is getting steeper over time. It is accelerating
Acceleration in a P-T Graph + acceleration - acceleration
Visualizing Motion: Velocity and Time
VELOCITY vs TIME GRAPH You just finished designing your own Hot Wheels car and you are ready to race it down the driveway. You take out your stopwatch and record the time from start (zero) to the end of the driveway. You then calculated the speed and created a chart. Let s take a look at how your car did. What would a velocity vs. time graph look like with this data? Do it in your notes!
What does the slope of a velocity vs. time graph tell you? Remember: Slope = y change in speed = x change in time What else have we talked about that s formula is change in speed change in time? Acceleration = change in speed change in time So the slope of a speed vs time graph gives us acceleration!
-The graph shows a slope with a straight line. According to the graph, what does this tell you about the acceleration? Straight line, so same slope Your car accelerates the same amount every second (constant acceleration) -How much is your car accelerating every second?
What to know about the speed vs. time graph. *If you see a slope, you are seeing acceleration* A = upward slope = positive acceleration, speeding up B = downward slope = negative acceleration, slowing down C= No slope (completely horizontal) = zero acceleration, but constant speed, so object is still moving unless the line is at zero
Learning Check
Comparisons
Speeding Up While Falling What could cause this? Object being dropped!
Free Fall/Gravity on a P-T Graph Trajectory of a ball being thrown upward
Free Fall/Gravity on a P-T Graph What is happening at each point?
Free Fall/Gravity on a P-T Graph What is happening at: J: Slowing Down K: Slowing Down L: Slowing Down M: Stopped N: Speeding Up O: Speeding Up P: Speeding Up Gravity is fighting the upward motion of the object on the way up, so the acceleration is -9.8 m/s/s (negative) Gravity is making the object move faster on the way down so the acceleration is 9.8 m/s/s