Velocity, Acceleration & Free Fall Chapter 2 Velocity, Acceleration & Free Fall

Displacement Displacement – change in location ∆x = x2 – x1 Displacement ≠ Distance traveled

Are you moving???? Compared to what?????? Surface of earth; axis of earth; sun; milky way All depends on your frame of reference

Velocity – a Vector 2-part - magnitude (speed) and direction

Instantaneous vs. Average Velocity Instantaneous - the speed at any instant – Speedometer average - Total distance covered/Total time

Velocity calculations Velocity = Δdistance/Δtime Units – distance per time - m/s distance = velocity*time

Check Problems On May 29, 1988, Rick Mears won the Indianapolis 500 in 3.45 hr. What was his average speed (in mi/hr and m/s)? The slowest animal ever discovered was a crab found in the red sea. It traveled with an average speed of 5.70 km/yr. How long would it take this crab to travel 100 km? What is its speed in m/hr?

Check problems (cont.) Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his yodel echo back from the canyon floor 5.20 s later. Assume that the speed of sound in air is 340 m/s. How deep is the canyon at this location? On July 2, 1988, Steve Cram of Great Britain ran a mile in 3.81 min. During this amazing run, what was his average speed in a mile/min? Mile/hr? m/s?

Constant Velocity vs. Changing Velocity Can you feel a change in velocity? Speeding up - gas pedal Slowing down - brake Turning - steering wheel Constant speed and constant direction

Graphing – relationship between distance & velocity Distance vs. Time graphs Velocity vs. Time graphs

Velocity Velocity – rate at which distance is covered Velocity*Time = Distance; vt = d Slope of d vs. t graph is velocity

Acceleration - defined Acceleration – rate of change of velocity Acceleration = Δvelocity/Δtime How fast you are going faster, slower, or turning

Acceleration simple examples A Cheetah increases its velocity from 15 m/s to 30. m/s in 2.0 seconds. What is its acceleration? A Bugatti Veyron can go from rest to 60. miles per hour in 3.0 seconds. What is its acceleration? Cruising along at 50.0 km/hr you see a red light and brake to a stop in 4.00 seconds. What is your acceleration?

Instantaneous vs. Average At an instant – slope from V vs. t graph Average – total Δv/ total Δt

Graphical relationships D vs. t – slope is velocity V vs. t – slope is acceleration, area under the curve is distance traveled A vs. t – slope is jerk, area under the curve is final velocity http://phet.colorado.edu/simulations/sims.php?sim=The_Moving_Man

Constant acceleration Initial velocity + acceleration*time = final velocity vi + at = vf Simply add product of acceleration and time it is applied to initial velocity A lion is trotting along at 5 m/s when it sees a zebra. It accelerates at a constant rate of 4 m/s/s for 3 seconds. What is its final speed.

Finding distance - constant acceleration Find average velocity: vavg = (vi + vf)/2 Distance = vavg*time Together d = ½(vi + vf)*t A train leaves the station with a velocity of 12 m/s. 3 seconds later it has a velocity of 36 m/s. How far has it traveled (assuming constant acceleration)?

Const. Acc. equation summary vf = vi + at - don’t know d d = ½(vi + vf)*t - don’t know a d = vit + ½at2 - don’t know vf 5 variables, given 3, choose the right equation and solve for desired 1

Gravity – example of const. acc. Earth’s gravitational force produces an acceleration on all masses Gravitational acceleration (g) = 9.8 m/s2 Constant around surface of the earth Tennisball - graph

Gravity examples Use constant acc. Equations with g for your acceleration How fast is a skydiver going after 4.00 seconds? How far has a skydiver gone in 5.00 seconds? How long will it take a skydiver to fall 1.0000000 kilometer?

Problem Solving Strategy Read problem – get a sense of what is going on – sketch it if that is helpful Identify what quantities are given Identify what is being asked for Find the right equation and check that it can be used Rewrite equation to solve for desired quantity Substitute values into equation to get answer Check that answer has right units and makes sense