Continue on Warm Up page… 9/9 Convert the following: 3 days to seconds 10,095 m/sec to miles/sec 57 km/hr to m/sec

Describing Motion The Equations…

So how do we know an object is moving? An object is in motion if its position changes. The mathematical description of motion is kinematics. The simplest kind of motion an object can experience is uniform motion in a straight line or linear motion.

As the car moves, it often undergoes changes in speed As the car moves, it often undergoes changes in speed. For example, during an average trip to school, there are many changes in speed. Rather than the speedometer maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating.

What is the difference between distance and displacement? Distance: How far something travels (scalar quantity) Displacement: How far something travels in a given direction, the straight line distance from my start point to end point (vector quantity)

DISTANCE DISPLACEMENT What is the distance of the biker? What is the displacement of the biker?

A skier travels from A to B then to C then to D. What distance does she travel? 420 m What is her displacement at D? 140 m right of A

SCALAR vs VECTOR Quantities Scalars are quantities which are fully described by a magnitude (measurement) alone. Ex. Distance, speed, and time Vectors are quantities which are fully described by both a magnitude (measurement) and a direction. Ex. Displacement and velocity If she jogs from A to B to C Distance traveled Displacement = AC + CB + BC = 400 m. = 200 m right of A

Scalar vs. Vector Vector Vector Scalar Scalar Vector Scalar Quantity Scalar or Vector 10 m/s East 10 N to the right 35 mi/hr 13 sec. 67 yds North 25 meters Vector Vector Scalar Scalar Vector Scalar

Frame of reference Based on your perception…describing something that is moving and comparing it to something stationary Independent and dependent variable relationship What is frame of reference dependent on?

AVERAGE SPEED (scalar) If an object takes a time interval t to travel a distance d, then the average speed of the object is given by:   s dist t

PROBLEM SOLVING GUIDELINES • Make a list of given quantities (Data) • Convert units if needed • Make a sketch if necessary • Identify what is to be determined • Always solve the equation for the unknown • Be consistent with units • Check that the answer seems reasonable • Physics problems take practice – the more you do the easier it will be!

Duncan Phillips AMCHS ‘07 Example 1: A runner makes one lap around a 200 m track in a time of 25 s. What is the runner's average speed? Givens: Base formula/rule: Answer: Work: Diagrams: d = 200 m t = 25 s 8 m/s S = d t Unknown: S S = d t m s = 8 m/s Duncan Phillips AMCHS ‘07 ‘O6 State Gold Medal 1600 m

Example 2: According to the World Disk Federation, on April 8,2000, Jennifer Griffin threw a Frisbee for a distance of 138.56 m to capture the woman’s record. If the Frisbee was thrown horizontally with a speed of 13.0 m/s, how long did the Frisbee remain aloft? Givens: Base formula/rule: Answer:   Work: Diagrams: S = d t = 10.7 s S = 13.0 m/s d = 138.56 m t = ? t = d S = 138.56 m 13.0 m/s = 10.658

Example 3: A snail can move approximately 0. 30 meters per minute Example 3: A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in 15 minutes? Givens: Base formula/rule: Answer:   Work: Diagrams: S = d t = 50 m S = 0.30 m/min t = 15 min d = ? d = st =(15 min) (0.30m/min) = 50

AVERAGE VELOCITY (vector)   Average velocity is the displacement divided by the amount of time it took to undergo that displacement. The difference between average speed and average velocity is that average speed relates to the distance traveled while average velocity relates to the displacement. x=xf-xi (found by finding the difference) -xf means final (you may also see Xf) -xi means initial (you may also see Xi) -Need to have an origin/reference point V = displacement = x elapsed time t v x t

Example 1: A vehicle travels 2345m in 315 sec toward the evening sun Example 1: A vehicle travels 2345m in 315 sec toward the evening sun. What was its velocity?

Example 2: What is a vehicles displacement if it is traveling 120 km/hr north for 30 min?

Example 3: Houston is 200km away, how long will it take a southbound bicyclist traveling at 100 m/s?

Observe the animation of the three cars below Observe the animation of the three cars below. How would you describe the motion of the red car? the green car? the blue car? The rate at which velocity changes is ACCELERATION

Units: m/s2 ACCELERATION  Acceleration is the rate of change of velocity. The change in velocity ΔV is the final velocity Vf minus the initial velocity Vi.   Units: m/s2

A positive acceleration means an increase in velocity; a negative acceleration usually means a decrease in velocity (deceleration). Note that negative acceleration is in OPPOSITE direction of the velocity

Find the speed at the end of 5 s Example 3: An object starts from rest with a constant acceleration of 8 m/s2 along a straight line. Find the speed at the end of 5 s Givens: Answer:   Work: Diagrams: Vo = 0 m/s a = 8 m/s2 t = 5 s Vf = 40 m/s Vf = ? Vf = 0m/s + (8m/s2)(5s) Vf = 40 m/s

= 0.63 m/s2 Example 4: A truck's speed increases uniformly from 15 km/h to 60 km/h in 20 s. Determine the acceleration. Givens: Answer:   Work: Diagrams: vo = 15 km/h = 4.17 m/s vf = 60 km/h = 16.7 m/s t = 20 s = 0.63 m/s2 a = ? m/s s = 0.6265 m/s2

Example 5: A bus moving at a speed of 20 m/s begins to slow at a constant rate of 3.0 m/s2. How long before it stops? Givens: Answer:   Work: Diagrams: t = 6.67 s Vo = 20 m/s Vf = 0 m/s a = - 3 m/s/s t =? t = Vf – Vo a t = 0 – 20 m/s -3 m/s2 t = 6.6667 s