1 1- D Motion Kinematics “Motion in a Straight Line!”

2 KINEMATICS - the process of motion is integral to the description of matter characteristics! - all matter is moving - therefore a method must be formulated for accuracy!

3 Describe motion in a straight line Which car has the greatest velocity?BLUE Which car has a constant velocity?RED Which 2 cars have the same average velocity? RED and GREEN

4 DISTANCE vs. DISPLACEMENT 1. DISTANCE - defined as the magnitude or length of motion - NO DIRECTION INDICATED symbol = d 2. DISPLACEMENT - magnitude and direction of motion symbol = s

5 Speed Speed: The “rate” of change of distance covered. A rate is anything compared to time. In own words, how “fast”. distance Speed = time Typical units: mi/hr, km/hr, m/s...

6 Average Speed Total distance covered Average speed = total time SPEED d t

7 Instantaneous Speed: The speed of an object at any particular instant. The average speed and instantaneous speed may not be the same! A car that gradually speeds up more and more has an instantaneous speed that always changes..

8 Constant Speed An object could be moving at a steady rate. Thus, its average and instantaneous speed would be the same! GBS Physics - speed vs. velocity

9 SOME EXAMPLES 1. A motocross rider travels a total distance of 300 km during a race. It takes the rider 2.5 hours to travel this distance. What is the average speed of the rider? SOLUTION: AVE SPEED = Total Distance / time speed = 300 km / 2.5 hrs = 120 km/hr v d t

10 SOME EXAMPLES speed = 454 km / 7200s = m / 7200s = 63 m/s v d t A high speed train travels 454 km in 7200 seconds. What is the train’s average speed? Formula : v (speed) = d/t d t

11 Velocity Velocity and speed are often used interchangeably. They are not the same term though! Speed is a scalar quantity. It has a number value only. No direction. Velocity is a vector quantity. It has a size and direction.

12 Question: A car is traveling at a constant 60mi/hr in a circular path. Does it have a constant speed? Does it have a constant velocity?

13 Acceleration Acceleration: The rate of change in speed and/or direction (or velocity) How fast something speeds up, slows down, or turns.

14 If an object has a constant velocity, then its acceleration would be zero. If an object is slowing down, it is decelerating:

15 change in velocity acceleration = time interval Δv a = Δt Δ, Greek letter delta = change in GBS Physics - Acceleration

16 Change in Speed/Velocity Acceleration = total time Acc vv t Eq: a = ∆v or a = v f – v i ∆t t f - t i Units m, km, mi, ft, s 2 h. s h. s s 2 Always a distance unit divided by two units of time. Why?

17 Ex: A particular car goes from rest to 90km/hr in 10 sec, what is its acceleration? Δv = 90 km/hr Δt = 10 sec a = Δv/ Δt = 90 km/hr/10 sec =9 km/hr / sec notice units... This means its velocity is changing by 9km/hr every second it accelerates at that rate.

18 Velocity vs. Acceleration? If you are flying at a constant 500 mi/hr on a jet airplane, do you have a large velocity? A large acceleration?

19 2. The stealth fighter accelerates from 700 mph to 1200 mph in 10 seconds. What is the acceleration of the aircraft? Acceleration = change in velocity / time ( 1200 mph mph) / 10 s 50 mph/s ( 500 mph) / 10 s = Acc vv t

20 3. A toy car accelerates from rest to a speed of 100 m/s in 5 seconds. What is the acceleration? Acceleration = change in velocity / time (100 m/s - 0 m/s) / 5 s 20 m/s/s or 20 m/s 2

40m-20m 4 s-2 s = 20m / 2s = 10 m/s

22 GRAPHICAL REPRESENTATION OF VELOCITY slope - the slope of a displacement vs. time curve would be the velocity Time is always the independent or x-axis. Plot points and draw a line of best fit. Remember! Label axis with units, and title graph. DO NOT CONNECT DOTS! GBS Physics - position vs. time

23 Data Chart : Constant Velocity Elapsed time (seconds)Distance (meters) Copy the data chart and construct a Distance vs. Time Graph Answer on the next SLIDE

24 Graph: Constant Velocity

25

26 Data Chart Constant Acceleration! What type of motion? Elapsed time (seconds) Distance (meters)

27 Graph of Data: Constant Acceleration

28

29 Constant Velocity Positive Velocity Changing Velocity (acceleration)

30 Fast, Rightward (+) Constant Velocity Fast, Leftward (-) Constant Velocity

31 GRAPHICAL REPRESENTATION OF ACCELERATION slope - the slope of a velocity vs. time curve would be the acceleration GBS Physics - velocity vs time

32 Velocity Time Graph Elapsed time (seconds) Distance (meters) Velocity (m/s) Copy the data chart and construct a VELOCITY vs. TIME Graph

33

34 Uniform Acceleration : Velocity vs. Time Elapsed time (seconds) Distance (meters)

35

36 Positive Velocity Positive Acceleration Positive Velocity Zero Acceleration

37