Chapter 2 Motion in One Dimension (Kinematics)

2.1 Displacement and Velocity Distance is a measure of the total motion of an object (how far it has traveled) Displacement is the net distance and direction an object has traveled (straight line distance and direction from starting to ending point) o What’s your distance when you run two laps around a 400 m track? o What is your displacement? o How are they different?

What is the gecko’s displacement? ∆x = x f - x i ∆x = 85 cm – 25 cm ∆x = 60 cm

Displacement continued Displacement is not always equal to the distance traveled (if you move back and forth) Displacement can be positive or negative.

Speed We use the variable speed to describe how quickly something moves. Saying a race car, runner, or plane is “fast” is not enough to accurately describe its speed scientifically.

Speed v = d t Distance traveled (m) Time taken (sec) Speed (m/sec)

Calculate speed A bird flies 50 meters in 7.5 seconds. Calculate the speed of the bird in m/sec.

Calculate distance How far do you go if you drive for 2 hours at a speed of 100 kilometers per hour?

Calculate time and distance A space shuttle is traveling at a speed of 7,700 m/sec. How far does the shuttle travel in kilometers in one hour? At an altitude of 300 kilometers, the circumference of the shuttle’s orbit is 42 million meters. How long does it take the shuttle to go around the Earth one time?

Calculating Speed Why the letter v is used for speed... o We use the letter v to represent speed in a formula. o We already used the letter s for seconds Speed is a single measurement that tells how fast you are going, like 100 km/h. Velocity means you know both your speed and your direction.

Instantaneous Speed and Velocity Instantaneous speed is distance ÷ time interval o when the time interval is made very small

Average Speed Average Speed is the TOTAL DISTANCE divided by the TOTAL TIME o When is Average Speed = Instantaneous speed?

Velocity Average velocity is displacement divided by the time interval

2.2 Acceleration Acceleration measures the rate of change of velocity When an object speeds up or slows down it is accelerating. When an object is speeding up its acceleration is positive and when it is slowing down its acceleration is negative Acceleration movie

Constant Acceleration Constant acceleration is sometimes called uniform acceleration. A ball rolling down a straight ramp has constant acceleration. constant acceleration increasing speed

Acceleration and Speed An object can have acceleration, but no speed. Consider a ball rolling up a ramp. As the ball slows down, eventually its speed becomes zero. constant negative acceleration decreasing speed

Speed vs Velocity We frequently use the terms speed and velocity interchangeably But remember that velocity is speed in a particular direction So speed is always a positive number Whereas velocity can be a negative number if you are going backwards.

Slope and Acceleration Use slope to recognize when there is acceleration in speed vs. time graphs. o Level sections (A) on the graph show an acceleration of zero. o The highest acceleration (B) is the steepest slope on the graph. o Sections that slope down (C) show negative acceleration (slowing down).

Slope of a graph The slope of a graph is equal to the ratio of rise to run. The rise is the amount the speed changes. The run is the amount the time changes.

Acceleration and slope Acceleration is the change in speed over the change in time. The slope of a speed vs time graph is acceleration.

Calculating Acceleration

Acceleration units Acceleration is a unit of distance divided by a unit of time squared. In physics we generally use the unit: m/s 2 (meters per second per second)

Kinematics Equations You should now know how to calculate average velocity and average acceleration using the equations for velocity and acceleration. Next we will combine them so that you can solve any problem related to objects that are moving at a constant velocity or accelerating. We need 3 more equations to do this.

Finding displacement (∆x) when you know initial and final velocity and time

Question: A sports car accelerates from rest to a velocity of 25 m/s in 5.0 seconds. How far did it travel?

Finding displacement (∆x) when you know initial velocity, acceleration, and time.

Question: A car traveling at 30 m/s brakes for 3.0 seconds at an acceleration of -2.0 m/s 2. How far did it travel during this time?

Finding final velocity when you know initial velocity, acceleration, and time

Question: A jet plane accelerates from rest down a runway for 12 seconds at an acceleration of 15 m/s2. What is it’s final velocity?

Using the Equations of Kinematics Choose a positive direction Draw a picture Make a chart of initial conditions Choose an equation to solve for the unknown Solve and check answer for reasonability

Kinematics Example #1 A car accelerates from a stop light for 20.0 s with an acceleration of 5.0 mph/s 2. Find its velocity at the end of this time. How far has it traveled?

Kinematics Example #1 V = 100 mph X = miles

Kinematics Example #2 A 747 airliner needs to achieve a speed of 360 km/h to take off. If acceleration is uniform and the runway is 1.8 km long, what acceleration is needed?

Kinematics Example #2 10 km/h/s or 2.78 m/s 2

Kinematics Example #3 A penny is dropped from a building rooftop and takes 6.0 s to hit the ground. What velocity does it hit the ground with? How tall is the building in meters? in feet? How would this change if you accounted for the speed of sound?

Kinematics Example #3 H=176m = 579ft V=58.8 m/s

Example #4 A High Speed Chase In a high speed chase, a police car takes off after a getaway car going at its maximum speed of 90 mph. The police car accelerates at a rate of 10 mph/s to a maximum speed of 120 mph. How long does it take to catch the bad guys?

Free Fall An object is said to be in “free fall” if it experiences only a force of gravity. o We abbreviate the accel. of gravity as “g” o g=9.81m/s 2 near the Earth’s surface

What goes up… A ball is tossed in the air.. o When is its velocity 0? o When is its acceleration positive? Negative?

Kinematics Example # 4 A ball is thrown straight up in the air with an initial velocity of 25.0 m/s. How long will it take for the ball to reach its starting point? What will the ball’s velocity be when it returns to its starting point?

Kinematics Example # 6 t = 5.08 s v f = m/s

The End…