Study of the Motion of Objects MECHANICS Study of the Motion of Objects Kinematics Description of HOW objects move Dynamics Study of forces and WHY objects move the way they do!

Kinematics -- One Dimension ***LINEAR MOTION*** Key Concepts: Motion is “Relative”!!! Distance vs. Displacement Speed vs. Velocity Average Velocity Acceleration

Motion is Relative How fast do you drive to school? How fast do you walk? A little boy claims that his Mom can drive him to school at 72,000 miles per hour! Explain. How fast does a person walk from the back of the train toward the front of the train? Earth travels through space at 20 miles/s (72,000 miles / hr); Assume the train is traveling at 50 miles per hour (person walks 3-4 miles per hour) = 53 miles per hour. My son takes a poll and finds that most people drive to school at a speed of ~ 30 miles per hr. But he claims that Mom gets him there at 72,000 miles per hour!!! Explain!

Relationships: Distance and Speed Average Speed: The distance an object travels divided by the time it takes to travel that distance Speed = Distance traveled / Time of travel v = Δd / Δt Units: eg, mph, km/h, m/s, km/s

DEFINITIONS Distance, Δd – change in position. Displacement, Δd – Change in position in a particular direction. NOTE ON DELTA NOTATION : Δ INDICATES THE CHANGE IN A QUANTITY.

Speed and Distance (con’t) Other equations for the speed and distance relationship (v = d / t): Distance = speed * time d = v * t Time = distance /speed t = d / v Distance Time Slope = speed

Position vs Time Graphs Graphical record of motion can be used to determine: “where” and “when” for an object – read position for a given time or read the time for a certain position average velocity of the object

Equation of motion from graph y = mx + b y: final position d1 m: average velocity v x: time t b: initial position d0 Create equation of motion from graph d1= 5t +20 When will rider be at position = -20 m?

Interpreting motion from graph Estimate the time when runner was at the 65 meter position. Draw interpolation lines – start at 65 meters  graph line  draw line down to 6.5 seconds

Slope of Position – Time Graph displacement = rise slope of position vs time graph = average velocity vavg = 4 m/s slope calculations must take actual value not boxes  boxes

What is Velocity?? Velocity is a Vector!! “Speed in a given direction!” “Displacement per time interval” “Change in position divided by the change in time” v (average) = Dd / Dt D “means change” = (final position – initial position) (final time – initial time) OR, Dd = v (average) x Dt Velocity Units: eg, mph, km/h, m/s, km/s Position Time Slope = velocity Δd

DEFINITIONS Speed, v – time rate of change of position. Velocity, v – Speed in a particular direction.

the total distance traveled The Big Idea Displacement is a change of position in a certain direction, not the total distance traveled

In one dimensional motion, the displacement direction is often given as positive, +, or negative, -. A displacement of +3.5 m implies movement of 3.5 m in the positive direction. A displacement of -3.5 m implies movement of 3.5 m in the negative direction. Positive and negative directions are chosen arbitrarily, but usually agree with standard mathematical conventions.

Average Velocity Other Equations: Also, and, Previously, v (average) = Dd / Dt and, Dd = v (average) Dt Also, v(average) = (final velocity + initial velocity) / 2

The “sign” of the velocity indicates the direction of movement. A positive sign indicates movement in the positive direction. A negative sign indicates movement in the negative direction.

Distance vs. Displacement Distance -- Length covered Displacement -- Change in position; straight line difference in starting position and ending position Start, A B C D 10 m 5 m Distance Displacement A to B 10 10 A to C 15 11 A to D 25 5 One full loop 30 0

The position of any object must be given with respect to some reference point. An object’s position is its directed distance from a reference point. Movement is said to have occurred when the position of an object with respect to a given reference point has changed.

Speed vs. Velocity Give examples of Speed vs. Velocity… Do two cars traveling at the same speed have the same velocity? Car “A” goes from Toronto to Ottawa; Car “B” goes from Ottawa to Toronto . Can a car can be going at a high speed but have zero velocity! Explain. Give an example. If both cars traveled 1 complete loop of a track at 50 mph, what was their avg. speed? What was their avg. velocity? A car moves at a constant speed of 40 mph. Describe its velocity.

Velocity is the slope of a position vs. time curve. Since slope = rise/run, Just as ,

What is Uniform Velocity? Means “constant” velocity – Velocity is the same at every point in time Neither speed nor direction changes!!!! Give examples traveling at uniform velocity… To school? On race track? Down the hall? Velocity Time Slope = 0 Cannot go in circle at constant velocity – direction changes!

Velocity vs. Time

What is Instantaneous Velocity? The velocity at any particular point in time (i.e., at a specific instant in time) Consider a drive to school, with varying velocities… Velocity (km/h) Time (hr) Average Velocity

Velocity problem Toby watches his pet iguana move from 4. 0 m S to 12 Velocity problem Toby watches his pet iguana move from 4.0 m S to 12.0m S and finds that the times for this motion were: to = 5.0s and t1=18.0 s Find the average velocity

Try the problems given .