Representing Motion

Motion We are looking to ____________and ____________an object in motion. Three “rules” we will follow: –The motion is in a __________________ –The _________of the motion is ignored (coming soon!) –The objects considered is a __________(not for long!) Particles and particle like objects move uniformly –Ex. __________________ –ANTI Ex. _______________________

Position The ____________of the particle in space. Needs a ______________description to be useful. We assign a ___________to represent the particles position on a coordinate grid. –There needs to be a ______point to reference –The positions to the left are ___________ –The positions to the right are ____________

Distance _________: The total path length when moving from one location to another –__________ Has only magnitude (i.e. size) and unit (NO DIRECTION) Other scalars: mass, time, energy

Displacement Displacement: the straight-line ____________between two points, along with the ____________from the starting point to the finish point –Vector: Has a ____________, unit, and direction Other vectors: acceleration, momentum, etc. Ex. 23 m/s [W] or -23 m/s

Displacement cont’d Position: x (m) Displacement: ______________________ +x→ ← -x +x→ ← -x

Displacement vs. Distance +x→ ← -x +x→ ← -x

Speed Speed: ______which distance is traveled –Average Speed ( ): The distance, d, traveled over the total time of the trip _______________________ –Instantaneous speed: speed at a particular instant

Speed cont’d Instantaneous or Average Speed?

Speed cont’d Example 1: A car is moving at a constant speed. If the car traveled a distance of 60 meters in 4 seconds: a) Find the speed of the car At the 60 meter mark, the car suddenly slows down to rest over 3.5 seconds and covers another 15 meters in doing so. b) Find the average speed of the car over the course of the entire problem

Velocity Velocity: how fast something is moving and in which ____________ ___________________ Direction of velocity is determined by the direction of the _______________

Instantaneous Velocity Instantaneous velocity: How fast something is moving at a ___________time (w/ a direction) Defined later as the ________of a position- time (x vs t) graph

Graphing Motion Carl Lewis ‘88Usain Bolt ‘ m1.89 s1.85 s m2.96 s2.87 s m3.90 s3.78 s m4.79 s4.65. s m5.65 s5.50 s m6.48 s6.32 s m7.33 s7.14 s m8.18 s7.96 s m9.04 s8.79 s m9.92 s9.69 s

Bolt ‘08 vs. Lewis ‘88

Position (x) vs Time Graphs 30 m 40 m50 m60 m20 m10 m0 m 3 s 4 s5 s6 s2 s1 s0 s X(m) t(s) 0 m 0 s 6 s 60 m x(m)t(s)

Avg Velocity vs Instantaneous Velocity On a Position vs. Time graph: –Avg _________is the displacement divided by time interval over which it occurred –Instantaneous velocity is the ______of a line at a given point If the slope is constant along a line segment Avg. Velocity = Inst. Velocity If the slope is changing v inst = slope of a line ___________at a given point. X(m) t(s) 5

1.position at t = 7 s 2.distance from 2 to 4 s 3.distance from 0 to 5 s 4.displacement from 0 to 4 s 5.displacement from 0 to 3 s 6.Time interval where speed is changing 7.speed at t = 2.5 s 8.instantaneous speed at t = 4 s 9.average velocity from 3 to 7 s 10.average speed from 0 to 8 s

Graphing Summary up to now x(m) t(s) Straight line means NO acceleration x(m) t(s) Curved line means changing slope which means changing ____________

Interpreting a VvT Graph v(m/s) t(s) +, ___________velocity v(m/s) t(s) +, ___________velocity v(m/s) t(s) +, ___________velocity v(m/s) t(s) -, ___________velocity v(m/s) t(s) -, ___________velocity

Interpreting a VvT Graph v(m/s) t(s) v(m/s) t(s) v(m/s) t(s) v(m/s) t(s) If the line is in the positive (+) portion of the graph the object is moving ________(i.e., + direction) If the line is in the negative (-) portion of the graph the object is moving ________(i.e., - direction)

Interpreting a VvT Graph v(m/s) t(s) v(m/s) t(s) If the line passes from the one region (+ to – or – to +) to another, the object changes _______________

Time (s) v (m/s) Interpreting a Velocity vs. Time Graph The area under the curve is the objects _____________.

Interpreting a Velocity vs. Time Graph The area under the curve is the objects displacement. Time (s) v (m/s)

Interpreting a Velocity vs. Time Graph The area under the curve is the objects displacement. Time (s) v (m/s)

What is the displacement from 0s to 2s? What is the displacement from 6s to 7 s? What is the displacement from 8s to 10s?

What is the total displacement?

Interpreting a VvT Graph The slope of a line on a VvT graph indicates acceleration (unit: m/s 2 ). __________________ _____________________ Time (s) v (m/s)

Acceleration Acceleration: The time rate of change of velocity Vector (has magnitude and direction) Unit: __________ The slope of a line on a velocity vs. time graph

Visualizing Acceleration

Practice Problem The United States Bowling Congress conducted a study on ideal bowling ball speed. It was found that a bowling ball should leave the hand going 9.4 m/s. If the ball goes from being at rest to 9.4 m/s in 1.5 seconds what is the acceleration of the ball?

Practice Problem A man starts from rest and is accelerated at a rate of m/s 2 over a time interval of.75s. What was his final velocity?

Acceleration Expressed in g’s –When accelerations are _________we express them as a multiple of “g” It is the ___________due to gravity near the surface of the Earth

Constant Acceleration This is a special case that tends to simplify things. _______________, or mostly constant, acceleration occurs all the time. –Car starting from rest when a light turns green –Car braking at a light when a light turns red There are a set of _________that are used to describe this motion.

Kinematic Equations

Constant Acceleration Problem A car starts from rest and accelerates uniformly to 23 m/s in 8 seconds. What distance did the car cover in this time?

Graphical Look at Motion: displacement – time curve The _______of the curve is the velocity The curved line indicates the __________is changing –Therefore, there is an _______________

Graphical Look at Motion: velocity – time curve The slope gives the ___________ The straight line indicates a __________acceleratio n

The zero slope indicates a ___________acceleration Graphical Look at Motion: acceleration – time curve

Test Graphical Interpretations Match a given velocity graph with the corresponding acceleration graph

Free Fall Acceleration This is a case of constant acceleration that occurs ___________. All things fall to the Earth with the same ___________ _____________________ –In the absence of air ________________, all things fall to the Earth with the same acceleration: –This is invariant of the objects dimensions, density, weight etc. When using the kinematic equations we use –a y = -g = m/s 2

Free Fall – an object dropped Initial velocity is zero Let up be positive Use the kinematic equations –Generally use y instead of x since vertical Acceleration is –a y = -g = m/s 2 _____ ______

Free Fall – an object thrown downward a y = -g = m/s 2 Initial velocity  0 –With __________being positive, initial velocity will be negative ______

Free Fall -- object thrown upward Initial velocity is upward, so ____________ The instantaneous velocity at the _____________height is zero a y = _______________everywhere in the motion v = 0 ______

Thrown upward, cont. The motion may be __________ –Then t up = t down –Then v = -v o The motion may not be symmetric –Break the motion into various parts Generally up and down

Free Fall Example Initial velocity at A is upward (+) and acceleration is ______________ At B, the velocity is 0 and the is ________________ At C, the ______________has the same magnitude as at A, but is in the opposite direction The ________________is –50.0 m (it ends up 50.0 m below its starting point)

Vertical motion sample problem A ball is thrown upward with an initial velocity of 20 m/s. –What is the max height the ball will reach? –What will the velocity of the ball be half way to the maximum height? –What will the velocity of the ball be half way down to the hand? –What is the total time the ball is in the air?