MOTION

Chapter Four: Motion 4.1 Position, Speed and Velocity 4.2 Graphs of Motion 4.3 Acceleration

4.1 Position, Speed and Velocity The origin is the place where position equals 0. The position of this car at 50 cm describes where the car is relative to the track. Position is a variable given relative to an origin.

4.1 Position, Speed and Velocity Position and distance are similar but not the same. If the car moves a distance of 20 cm to the right, its new position will be 70 cm from its origin. Distance = 20 cm New position

4.1 Position, Speed and Velocity The variable speed describes how quickly something moves. To calculate the speed of a moving object divide the distance it moves by the time it takes to move.

4.1 Position, Speed and Velocity The units for speed are distance units over time units. This table shows different units commonly used for speed.

4.1 Average speed When you divide the total distance of a trip by the time taken you get the average speed. On this driving trip around Chicago, the car traveled and average of 100 km/h.

4.1 Instantaneous speed A speedometer shows a car’s instantaneous speed. The instantaneous speed is the actual speed an object has at any moment.

Solving Problems How far do you go if you drive for two hours at a speed of 100 km/h? Looking for: …distance Given: …speed = 100 km/h time = 2 h Relationships: d = vt Solution: d = 100 km/h x 2 h = 200 km = 200 km

4.1 Vectors and velocity Position uses positive and negative numbers. Positive numbers are for positions to the right of the origin and negative numbers are for positions to the left the origin.

4.1 Vectors and velocity Distance is either zero or a positive value.

4.1 Vectors and velocity We use the term velocity to mean speed with direction.

4.1 Keeping track of where you are Pathfinder is a small robot sent to explore Mars. It landed on Mars in 1997. Where is Pathfinder now?

4.1 Keeping track of where you are Pathfinder keeps track of its velocity vector and uses a clock. Suppose Pathfinder moves forward at 0.2 m/s for 10 seconds. What is Pathfinder’s velocity?

4.1 Keeping track of where you are Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds. What is Pathfinder’s change in position?

4.1 Keeping track of where you are The change in position is the velocity multiplied by the time.

4.1 Keeping track of where you are Each change in position is added up using positive and negative numbers. Pathfinder has a computer to do this.

4.1 Maps and coordinates If Pathfinder was crawling on a straight board, it would have only two choices for direction. Out on the surface of Mars, Pathfinder has more choices. The possible directions include north, east, south, and west, and anything in between.

4.1 Maps and coordinates A graph using north−south and east−west axes can accurately show where Pathfinder is. This kind of graph is called a map. Street maps often use letters and numbers for coordinates.

4.1 Vectors on a map Where are you compared to where you started? Suppose you run east 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 to where you started?

4.1 Vectors on a map To get the answer, you figure out your east−west changes and your north−south changes separately. origin = (0 , 0)

4.1 Vectors on a map Your first movement has a velocity vector of +2 m/s, west-east (x-axis). After 10 seconds your change in position is +20 meters (east on x-axis). d = v x t d = 2 m/s x 10 s = +20 m

4.1 Vectors on a map Your second movement has a velocity vector of −2 m/s north−south (y-axis) In 10 seconds you move −20 meters (south is negative on y-axis) d = 2 m/s x 10 s = -20 m New position = (+20 , -20)

Solving Problems 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? Looking for: …train’s new position Given: …velocity = +100 km/h, east ; time = 4 h …velocity = -50 km/h, west ; time = 4 h Relationships: change in position = velocity × time

Solution: Solving Problems 1st change in position: (+100 km/h) × (4 h) = +400 km 2nd change in position: (−50 km/h) × (4 h) = −200 km Final position: (+400 km) + (−200 km) = +200 km The train is 200 km east of where it started.

4.3 Curved motion Circular motion is another type of curved motion. An object in circular motion has a velocity vector that constantly changes direction.