Change in Velocity Each time you take a step you are changing the velocity of your body. Each time you take a step you are changing the velocity of your body. You are probably most familiar with the velocity changes of a moving bus or car. You are probably most familiar with the velocity changes of a moving bus or car. The rate at which velocity (speed or direction) changes occur is called acceleration. The rate at which velocity (speed or direction) changes occur is called acceleration.

Acceleration= final velocity- starting velocity Acceleration= final velocity- starting velocity time time Change in velocity = final – starting velocity velocity Change in velocity = final – starting velocity velocity Acceleration= change in velocity Acceleration= change in velocity time time

Acceleration = Velocity (final) - Velocity (original) time A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? = 90 mph - 60 mph 3 seconds = 30 mph 3 seconds = 10 mph/second

Positive acceleration Negative acceleration

Acceleration = Velocity (final) - Velocity (original) time A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? = 0 mph - 60 mph 6 seconds = - 60 mph 6 seconds = - 10 miles per hour per second

- A constant acceleration produces a straight line or linear slope (rise/run). - The slope of a non- linear velocity-time graph (rise/run) will predict an objects instantaneous acceleration. a = v/t - A constant acceleration produces a straight line or linear slope (rise/run). - The slope of a non- linear velocity-time graph (rise/run) will predict an objects instantaneous acceleration. a = v/t

Free fall The constant acceleration of an object moving only under the force of gravity is "g". The constant acceleration of an object moving only under the force of gravity is "g". The acceleration caused by gravity is 10 m/s 2 The acceleration caused by gravity is 10 m/s 2 If there was no air, all objects would fall at the same speed If there was no air, all objects would fall at the same speed Doesn’t depend on mass Doesn’t depend on mass After 1 second falling at 10 m/s After 1 second falling at 10 m/s After 2 seconds 20 m/s After 2 seconds 20 m/s 3 seconds 30 m/s 3 seconds 30 m/s

Galileo 1600’s 1600’s Studied how things fell Studied how things fell Didn’t have a good clock Didn’t have a good clock Rolled balls down an inclined plane Rolled balls down an inclined plane Found that the speed increased as it rolled down the ramp Found that the speed increased as it rolled down the ramp

Galileo t = 0 t = 1 second t = 2 seconds t = 3 seconds Acceleration= change in velocity time time

Galileo u Same things happen when things fall u Didn’t drop things from Tower of Pisa

v 2 final = 2gd y A final velocity can be calculated over a vertical displacement “d y " during free fall using the equation: A final velocity can be calculated over a vertical displacement “d y " during free fall using the equation:

d y = 1/2 gt 2 The vertical displacement “d y " that occurs during a specific time of free fall can be determined using the equation: The vertical displacement “d y " that occurs during a specific time of free fall can be determined using the equation: Or a time interval can also be determined over a specified distance of freefall using the equation: Or a time interval can also be determined over a specified distance of freefall using the equation: t 2 = 2d y /g

Falling Air resistance will increase as it falls faster Air resistance will increase as it falls faster An upward force on the object An upward force on the object Eventually gravity will balance with air resistance Eventually gravity will balance with air resistance Reaches terminal velocity - highest speed reached by a falling object. Reaches terminal velocity - highest speed reached by a falling object.

Terminal velocity Force of gravity is constant Force of gravity is constant u air resistance increases as you speed up u until the force is equal u Equal forces, no acceleration u constant velocity terminal velocity