CHAPTER 4 MOTION 4 1 POSITION SPEED VELOCITY

CHAPTER 4 MOTION

4. 1 POSITION, SPEED, VELOCITY

VOCABULARY • Position – a variable that tells location relative to origin • Origin – a place where the position has been given a value of zero • Speed – how quickly an object moves • Instantaneous Speed – the actual speed of a moving object at any moment

THE POSITION VARIABLE • Position Vs Distance – The distance of the car from the origin is 50 cm – The position of the car is 50 cm to the right of the origin You cannot have negative distance.

SPEED • If you drive 120 miles (the distance) and it takes you 2 hours (the time) your speed is 60 miles per hour (120 mi/2 hr = 60 mph) • Think about a road trip, your average speed might be 70 mph, but maybe there was traffic (speed = 15 mph) or maybe you were speeding at one point (speed = 80 mph). This is the difference between average speed and instantaneous speed.

SPEED • How far will you go if you drive for 2 hours at a speed of 100 km/h? • You travel at an average speed of 20 km/h in a straight line to get to your grandmother’s house. It takes you 3 hours to get to her house. How far away is her how from where you started? • What is the speed of a snake that moves 20 meters in 5 seconds? • A train is moving at a speed of 50 km/h. How many hours will it take the train to travel 600 kilometers?

VOCABULARY • Vector – a variable that gives direction information • Velocity - a variable that tells you both speed and direction

VECTORS AND VELOCITY • Position is an example of a vector – it tells you direction and an amount • Moving forward is represented with a positive, moving backward is represented with a negative • Velocity is speed with direction • Velocity is a vector, speed is not

MAPS AND COORDINATES • One way to describe is to use a coordinate grid (think north and south as the y-axis and east and west as the x-axis) • A graph that displays these axis is called a map • Suppose you run easy for 10 seconds at a speed of 2 m/s. Then you turn and run south at the same speed for 10 more seconds. Where are you compared with where you started?

PROBLEMS: VELOCITY • A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?

CLASSWORK • P 86 # 1 - 8 • Demonstrate Motion and Shoot the Monkey Gizmo

4. 2 MOTION GRAPHS

VOCABULARY • Constant Speed – speed that stays the same • Slope – is the ratio of the rise (vertical change) to the run (horizontal change)

POSITION VS TIME GRAPH • This is a position vs time data because it tells you the runner’s position at different points in time. What is the runner’s constant speed?

GRAPHS SHOW RELATIONSHIPS BETWEEN VARIABLES • The image to the left shows you the relationship between the angle of the racetrack and the speed of the car • The graphs above show a weak or no relationship between variables.

SPEED VS TIME GRAPH The graphs below show two runners in a race: • What similarities and differences are shown in the two graphs? • How can you tell the speed from the first graph? • How can you tell the distance from the second graph?

CLASSWORK • P 91 # 1 - 9 • Demonstrate Distance -Time Graph Gizmo

4. 3 ACCELERATION

VOCABULARY • Acceleration – the rate at which velocity changes • Free Fall – accelerated motion that happens when an object falls with only the force of gravity acting on it • Acceleration Due to Gravity – the value of 9. 8 m/s 2, which is the acceleration in free fall at Earth’s surface, usually represented by a small letter g • Projectile – an object moving through space and affected only by gravity

ACCELERATION • Think about pressing the gas pedal, the car speed increases • If you press the brakes, the car slows down • Acceleration describes changes in speed or velocity

ACCELERATION • Think about going up bicycling down a hill, at the top you move slowly but towards the bottom you are move must faster as you accelerate • The acceleration depends on the steepness of the hill

SPEED AND ACCELERATION • Acceleration describes how quickly speed changes

SPEED AND ACCELERATION • A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 seconds. Calculate the acceleration. • Calculate the acceleration of an airplane that starts at rest and reaches a speed of 45 m/s in 9 seconds. • Calculate the acceleration of a car that slows from 50 m/s to 30 m/s in 10 seconds.

ACCELERATION MOTION GRAPHS • Positive Acceleration shows things getting faster • Negative Acceleration shows things getting slower (Deceleration) • It is curved because it is increasing speed each second

FREE FALL • Think of a ball, as soon as it leaves your hand it is in free fall because essentially the only force acting on it is gravity • If the air friction is ignored the force of gravity will increase the speed 9. 8 m/s every second.

FREE FALL • Constant acceleration mean’s an object’s speed changes by the same amount each second

ACCELERATION AND DIRECTION • If an object’s acceleration is zero the object can only move at a constant speed in a straight line (or be stopped) • Acceleration occurs whenever there is a change in speed, direction, or both.

CURVED MOTION • Curved motion is caused by sideways accelerations • This causes the velocity to change direction, which results in turning, creating curved motion • A soccer ball is an example of a projectile, moving under the influence of gravity

CLASSWORK • P 99 #2 -11