Motion. Slope. Slope. Distance and Displacement

Transcription

1 Steepness or slope base (run), height (rise) slope = rise/run slope down (\) : - (rise/run) slope up (/) : + (rise/run) sudden change of slope curved hill - the slope is always changing procedure to find a slope of a curved hill - slope method tangent line Motion Slope Given 2 points (x 1,y 1 ) and (x 2,y 2 ) the slope of the straight line going though them is: Slope Distance and Displacement Slope of a vertical line Slope of a horizontal line y=mx+b m slope b - y-intercept Distance and displacement are two quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions. Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

2 Speed and Velocity Speed is a scalar quantity which refers to "how fast an object is moving." Instantaneous speed: the speed in an instant Average speed = total distance covered / duration Velocity is a vector quantity which refers to "the rate at which an object changes its position." Acceleration how does the velocity change, vector quantity Velocity: speed + direction of motion: 60 km/h to the North Constant velocity or constant speed -- equal distances are covered for equal intervals of time. Constant velocity means constant speed with no change in the direction of motion. Velocity vector -- a pictorial way to represent velocity -- an arrow drawn to scale that represents the magnitude and direction of a given velocity Any quantity that is described by magnitude and direction Velocity vector: magnitude=speed, direction= N, S, E, W, etc Vectors can be added and subtracted - new vector - resultant Vectors that act along a parallel directions Vectors not parallel to each other - parallelogram rule: parallelogram with the two vectors as adjacent sides, with tails together - the diagonal is the resultant Steady motion -- velocity does not undergo changes Accelerated motion -- velocity undergoes changes We change the velocity if we change the speed and/or the direction Acceleration is the rate of change in velocity: Acceleration = change of velocity / time interval Acceleration can increase or decrease the velocity: positive or negative acceleration

3 Car moving with a constant velocity of +10 m/s for 5 seconds. Motion in a curved path -- we accelerate even when we move with constant speed Stand up during a buss ride -- difference between velocity and acceleration Motion along a straight line -- speed = velocity: acceleration = change is speed / time interval Speed increases -- acceleration is in direction of velocity Speed decreases -- acceleration is opposite to velocity the slope of the line (10 m/s) is the same as the velocity of the car 2004 The Physics Classroom and Mathsoft Engineering & Education, Inc. The Meaning of Slope for a p-t Graph a small slope means a small velocity a negative slope means a negative velocity a constant slope (straight line) means a constant velocity a changing slope (curved line) means a changing velocity

4 Slow, leftward (-) Fast, leftward (-) car moving with a changing, rightward (+) velocity: that is, a car that is moving rightward and speeding up or accelerating. Slow, Rightward (+) Fast, Rightward (+) Positive Velocity Positive Velocity Changing Velocity (acceleration) If an object is slowing down, then its acceleration is in the opposite direction of its motion. If an object is speeding up, then its acceleration is in the same direction as its motion. a<0 a>0 Leftward ( ) Velocity Slow to Fast Acceleration same direction as the motion Leftward ( ) Velocity Fast to Slow Acceleration opposite to motion

5 Object, free of all restraints, falls under the influence of gravity alone during each second of free fall an object gains a speed of 10 m/s free fall acceleration is about 10 m/s 2 For an object falling from rest the instantaneous velocity is All objects fall equally fast!!! If there is no air resistance For uniform acceleration Distance traveled = 1/2 acceleration x time x time For free-fall d=1/2 gt 2 Distance Fallen in Free-Fall Time of Inst. Speed Distance of Fall (s) (m/s) Fall (m) at at at at at t 10 t t 2 During time interval 0 to1 s: Average speed =(0+10)/2 = 5 m/s At the end of the first second the distance fallen is 5 m