Acceleration Due to Gravity Free fall - falling under influence of gravity w/o ______ ____________ Distance proportional to time squared Speed changes linearly with time The ____________________________ is the same for all objects and is often represented by the letter ____ g = 9.8 m/s2 toward the Earth. air resistance acceleration due to gravity g

Falling objects zero 9.8 m/s2 symmetry The velocity at the top of the path is _______ The acceleration of the object throughout the motion is always ____________ Trajectories show up and down ____________ zero 9.8 m/s2 symmetry

Falling objects For a falling body, a = g = 9.8 m/s2 down

Falling objects Notice that the distance the object falls during each second is larger than the distance that it fell in the previous second… WHY?

Air Resistance and Freefall

Terminal Velocity

Acceleration Due to Gravity d = ½ at2 vf = vi + at a = g = 9.8 m/s2 down or -9.8 m/s2 Remember that if up is labeled as the ________________, down must be labeled as the ________________ The velocity at the top of an object’s path is _____ when it is in __________. positive direction negative direction zero freefall

An object is dropped from the top of the Willis Tower, which is 443 meters tall. How long will it take the object to reach the ground? How fast is the object travelling when it lands on the ground? d = ½ a t2 d = - 443 m a = - 9.8 m/s2 - 443 m = ½ (-9.8 m/s2) t2 t = ? - 443 m = (-4.9 m/s2) t2 t = 9.51 s vf = vi + a t d = - 443 m vf = 0 m/s + (-9.8 m/s2)(9.51 s) a = - 9.8 m/s2 vf = - 93.2 m/s t = 9.51 s Why is the answer negative? vf = ? Because the object is moving down! vi = 0 m/s

You work on some problems for ~15 min and then we will go into graphing.

Position-Time Graphs Show an object’s position as a function of time. x-axis: time y-axis: position We refer to them as position vs. time graphs because the convention is that the y-axis variable is given first and the x-axis variable is given second

Position-Time Graphs 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s Imagine a ball rolling along a table, illuminated by a strobe light every second. You can plot the ball’s position as a function of time. 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s

Position-Time Graphs 1 2 3 4 5 6 7 8 9 10 position (cm) time (s)

Position-Time Graphs What are the characteristics of this graph? Straight line, constant positive slope What kind of motion created this graph? Constant positive velocity 1 2 3 4 5 6 7 8 9 10 time (s) position (cm)

Position-Time Graphs Each type of motion has a characteristic shape on a P-T graph. Constant velocity (positive velocity and negative velocity have a similar shape) Zero motion (at rest) Accelerating (speeding up) Decelerating (slowing down)

Position-Time Graphs Constant velocity is represented by a straight line with a constant slope on the P-T graph. time (s) pos. (m) Constant speed in positive direction. time (s) pos. (m) Constant speed in negative direction.

Position-Time Graphs Zero speed is represented by a straight segment with a zero slope on the P-T graph. time (s) pos. (m) A horizontal segment means the object is at rest.

Position-Time Graphs Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Speeding up in positive direction. time (s) pos. (m) Speeding up in negative direction.

Position-Time Graphs Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Traveling in positive direction, but slowing down. time (s) pos. (m) Traveling in negative direction, but slowing down.

Position-Time Graphs The slope of a P-T graph is equal to the object’s velocity in that segment. slope = change in y change in x time (s) position (m) 10 20 30 40 50 slope = (30 m – 10 m) (30 s – 0 s) slope = (20 m) (30 s) slope = 0.67 m/s

Position-Time Graphs The following P-T graph corresponds to an object moving along in one dimension. Can you describe its movement based on the graph? time (s) position (m) N S

Velocity-Time Graphs A velocity-time (V-T) graph shows an object’s velocity as a function of time. A horizontal line = constant velocity. A straight line with non-zero slope = constant acceleration (no changing acceleration in this class) Acceleration = change in velocity over time. Positive slope = positive acceleration. Not necessarily speeding up! Negative slope = negative acceleration. Not necessarily slowing down!

Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. time (s) velocity (m/s) N S Object is moving at a constant velocity North.

Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. time (s) velocity (m/s) N S Object is moving at a constant velocity South.

Velocity-Time Graphs If an object isn’t moving, its velocity is zero. time (s) velocity (m/s) N S Object is at rest

Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction. If v is positive also, object is speeding up. The graph will be moving away from the x axis If v is negative, object is slowing down. The graph will be moving toward the x axis

Velocity-Time Graphs V-T graph has positive slope. N S time (s) velocity (m/s) N S Positive velocity and positive acceleration: object is speeding up! time (s) velocity (m/s) N S Negative velocity and positive acceleration: object is slowing down.

Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction. If v is positive, the object is slowing down. The graph will be moving toward the x axis If v is negative also, the object is speeding up. The graph will be moving away from the x axis

Velocity-Time Graphs V-T graph has negative slope. N S time (s) velocity (m/s) N S Positive velocity and negative acceleration: object is slowing down, time (s) velocity (m/s) N S Negative velocity and negative acceleration: object is speeding up! (in negative direction)