Language of Motion
8.1 Direction Makes a Difference Two main types of quantities: Scalars: Describe magnitude (size of a measurement) but not direction. Example: Johnny skateboarded 7 meters, Johnny skateboarded for 5 seconds. Distance - describes the length between 2 locations Vectors: Describe magnitude and direction. Example: Johnny skateboard 7 m East Position - a specific point relative to a point of origin Time interval (change in time) The time interval to move from the fire hydrant to the sign is calculated by: final minus the initial
Displacement describes how much an object’s position has changed. A car leaves home and drives 10 km to the store then returns home, what is its distance and displacement? The car has driven a total distance of 20 km but its final displacement is 0 km. Displacement describes how much an object’s position has changed. If the car leaves home and drives 10 km east to the store, what is its displacement? = 10 km [E] - 0 = 10 km [E] = + 10 km When using vector quantities, opposite directions are given opposite signs.
What is the person’s displacement & distance travelled between 0s and 15s? d = 15 m + 10 m + 20 m = 45 m = 10 m [W] – 5 m [E] = - 10 m – (+5 m) = - 15 m = 15 m [W]
Think you got it? Try This… What is her initial position? What is the distance she travelled? What is the time interval? What is her displacement from hydrant? d= 9 m [E] d= + 9 m d = 14 m t = 10 sec Δ d = 5 m [W] Δ d = - 5 m
Can create a table as follows: When a body covers equal distances in equal intervals of time then the body is said to have uniform motion. Roll a ball across a floor… 1 s 2 s 3 s 4 s 5 s 0 m 20 cm 60 cm 100 cm Can create a table as follows: Uniform motion creates a straight line on a position-time graph TIME (s) POSITION (cm) 1 20 2 40 3 60 4 80 5 100 Objects in uniform motion do not speed up, slow down or change direction
Which direction is the object moving? Forward On a position-time graph, the slope is equal to the velocity: A positive slope means moving away from origin at a uniform speed Zero slope means the object’s average velocity is zero (i.e. the object isn’t moving!) A negative slope means that the object’s average velocity is moving in the negative direction (i.e. the object is moving backwards at a uniform speed) Which direction is the object moving? Since right is given as a positive value, then a negative slope indicates the object is travelling to the left.
8.2 Average Velocity On a position-time graph the average velocity is the slope of the line Average Velocity of ball???? the rise is the change in position ( ) divided by the run which is the change in time ( ). vav = 80 cm - 40 cm 4 s - 2 s = 40 cm 2 s = 20 cm/s
Comparing Velocity Who is running faster and by how much? va = 16 m - 12 m 4 s - 3 s = 4 m 1s = 4 m/s vb = 10 m - 8 m 6 s - 4 s = 2 m 2 s = 1 m/s va - vb = 4 m/s – 1 m/s = 3 m/s
Calculating Velocity Speed - is relationship between the distance of an object per unit of time (scalar quantity), e.g. 60 km/h Velocity is a relationship between the displacement (speed and direction) of an object per unit of time (vector quantity), e.g. 60 km/h [N] Displacement & relationship between velocity, and time is given by: Time & relationship between displacement and velocity is given by:
Calculating Velocity 1) A boat is at rest and travels 280 m east in a time of 120 s. What is the boat’s average velocity? Vav = ∆d/∆t = 280 m east / 120 s = 2.33 m/s east 2) A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s? ∆d = vav * ∆t = 6.5 m/s * 12 s = 78 m 3) A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long? ∆t = ∆d/vav = 11 m / 15 m/s = 0.733 s 4) A car is travel at 30 m/s east and slows down to 20 m/s east in 5 s. What is the cars average velocity over those 5 s? Average velocity = V1 + V2 = 30 m/s + 20 m/s = 25 m/s 2 5) You drive 500 km east in 5 hours and 300 km east in 3 hours. What is the car’s average velocity? (500 km + 300 Km ) / 8 hours = 100 km/h