Measuring Motion Chapter 1

1.1: Position and motion How do you know an object is moving? When you watch the motion of an object, you are actually watching the object in relation to another object that appears to stay in place. The object that appears to stay in place is a reference point.

1.1: Position and motion A reference point is the starting point you choose to describe the location, or position, or an object The position of an object is its distance and direction from a reference point Motion is the process of changing position Common Reference Points: tree building door objects in motion – a bird flying while in a hot air balloon.

1.1: Position and motion Distance and Displacement Distance depends on the path taken Displacement is the difference between the initial (first) position and the final position of the object Always the _shortest_ path! Line Distance Displacement A B C D

1.2: Speed and Velocity Speed-Distance traveled by an object divided by the time taken to travel that distance.   The SI unit for speed is meters per second (m/s). Other units: mi/h, km/h, ft/s

1.2: Speed and Velocity Most of the time, objects do not travel at a constant speed – you probably do not walk at a constant speed from one class to the next. Average speed= total distance Total time

1.2: Speed and Velocity Examples: An athlete swims a distance from one end of a 50m pool to the other end in a time of 25s. What is the athletes average speed? Jake jogs to a store 72 m away with an average speed of 2 m/s. How long did it take Jake to run to the store?

1.2: Speed and Velocity A bee is flying by at a speed of .75 m/s. How far will the bee travel in 60 seconds?

1.2: Speed and Velocity Distance-Time graphs This type of graph is based on the most basic things we need to know about the motion of an object (__distance__ and ___time_). Time goes on the _X_ axis Position / Distance goes on the _Y_-axis IF the object moves __away_ from start, we _____increase____ distance (+) IF the object moves __toward_ start, we ___decrease_ distance (-) Draw each section a bit at a time No best fit lines!

1.2: Speed and Velocity Elements of a Distance-Time Graph Slowing down- ___decreasing__ (-) slope Stopping- _NO_ slope (horizontal line) Speeding up- ___increasing_ (+) slope Average speed- Find the distance changed and the time changed between a starting point and a stopping point.

1.2: Speed and Velocity

1.2: Speed and Velocity What is happening from 0-30 seconds? 105 to 120? 120 to 135? 135 to 150?

1.2: Speed and Velocity What is the speed of the dancer from… 30 to 60 seconds? 90 to 105 seconds? 135 to 150 seconds?

1.2: Speed and Velocity Velocity: Direction Matters Imagine that 2 students leave the same classroom at the same time. They both walk at 10km/hr for 5 min, 12 km/hr for 8 min, and 5 km/hr for 10 min. Why don’t they end up at the same place?

1.2: Speed and Velocity Velocity- Speed of an object in a particular direction You must always include a direction in your answer Constant velocity only occurs if neither speed nor direction changes. Velocities can be added or subtracted together to give a resultant velocity. Add velocities that are in the same direction. Ex: Walking on a bus as the bus is moving forward. Subtract velocities that are in opposite directions. Ex. Walking to the back of the bus while it is moving forward

1.2: Speed and Velocity Finding Resultant Velocities Same direction Resultant Velocity = 2 km/min east 15 km/min east

1.2: Speed and Velocity Opposite directions Resultant Velocity= 2 km/min west 15 km/min east

1.2: Speed and Velocity Equation: SI Unit: m/s (direction) Velocity = distance time EX 1: What is the velocity of a dog running 12 meters north in 2.5 seconds?

1.2: Speed and Velocity EX 2 EX 3 How long does it take a train traveling 30 m/s W to travel 150m? EX 3 If a bus travels 40 m/s E for 30s, how far does the bus travel?

1.3 Acceleration Acceleration is the rate at which velocity changes. Velocity changes if: speed changes direction changes both change Increase in velocity = positive acceleration Decrease in velocity = negative acceleration (deceleration)

1.3 Acceleration Calculating Average Acceleration Avg Accl = final velocity-starting velocity time it takes for velocity to change A = vf – vi = A = Δv t t Velocity is expressed in m/s and time is expressed in s. Therefore, acceleration is expressed in meters per second per second (m/s/s) or m/s2

1.3 Acceleration Equation: Calculation: 0 m/s 1 m/s 2 m/s 3 m/s 4 m/s 0:01 0:02 0:03 0:04 0:00 0 m/s 1 m/s 2 m/s 3 m/s 4 m/s Equation: Calculation:

1.3 Acceleration A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds.  What is the acceleration of the skater? A plane passes point A at a velocity of 240 m/s north. Forty seconds later, it passes point B at a velocity of 260 m/s north. What is the planes average acceleration?

1.3 Acceleration A car is traveling at 25 m/s and slows down to 10 m/s while making a turn that took 8 seconds. What was the cars acceleration? What is the change in velocity of a car that accelerated from a stop sign at 17 m/s2 in 9 seconds?

1.3 Acceleration How long will it take a car to go from 0 to 45 km/hr if they are accelerating at 5 km/hr2?

1.3 Acceleration Recognizing Acceleration on a Graph Velocity has to CHANGE over time

Section 3: Acceleration Speed-Time graphs X-axis is the same (_time_(s)) Y-axis is now __velocity (m/s)__ Elements of a speed-time graph Object at rest- horizontal line where __y=0__ Constant speed- __horizontal_ line Speeding up- _positive_ (+) slope Slowing down- __negative__ (-) slope