Solving Word Problems

1. Solving Word Problems • To solve a word problem, think: • numbers, question, formula, label • circle the numbers, read the question, write the formula and finally label the parts of the question that relate to the formula

2. Solving Word Problems – cont’d Let’s do a sample for density – follow the prompts • A sample of substance X has a density of 5 g/ml and a mass of 80 g. What is it’s volume? ---------------------------------------------------------------- • numbers • question • formula • label • Then, solve the equation. Volume = 80 g / 5 g/ml • Volume = 16 ml density mass Density = Mass / Volume Volume = Mass / Density

3. Speed & Velocity Unit 4 – Lecture 1

4. Motion • Kinematics – branch of science which describes motion [without describing the cause of the motion] • motion is measured as a change in position • distances can be positive or negative • depends on the frame of reference

5. Frame of Reference • the frame of reference depends on the observer • compares speed and angles of movement from the observer’s perspective and surroundings • explains the 75mph fly

6. Speed • Speed – how rapidly an object changes location • units of distance divided by units of time • ex: miles per hour, kilometers per hour, centimeters per month, etc. d distance d distance V speed = t time V speed t time

7. Practice • What is the speed of a runner that travels 250 m in 50 min? • 5 m/min. 0.2 m/min. 12,500 m/min. • How long does a trip of 3000 km take if you travel at 110 km/hr.? • 330000 hr. 0.037 hr. ~27 hr. • How far will a car traveling at 70km/hr. go in 2 hours? • 360 km 140 km 0.4 km 2.5 km 0.04 km • What is the speed of a bike that travels 12 km in 30 min.? • 360 km/hr 24 km/hr 0.4 km/hr 2.5 km/hr 0.04 km/hr • Average human walking speed is 5 km/hr. How far can you walk in two hours? • 10 km 10 km/hr. 10 hr. 10 km•hr. [none]

8. Types of Speed • Three types of speed [distance divided by time] • average speed • total distance divided by total time • instantaneous speed • how fast you’re going NOW • constant speed • speed that does not change • not really observed on earth – objects in orbit, etc.

9. More Practice What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s? If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km. (a) how far would it travel if it moved at this rate for 4 h? (b) for 10 h? 25 meters / second 25 meters / second 240 km 600 km

10. More Practice – cont’d In addition to speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one half hour later, what has been your average speed? Would it be possible to attain the average speed in previous example and never go faster than 80 km/h? 80 kilometers per hour No – in order to have an average, need to have speeds higher and lower . If you had a constant speed, this would work, however, that is not realistic for typical scenarios.

11. Velocity • Velocity describes the speed AND the direction of an object’s motion.

12. Types of Velocity • Instantaneous Velocity • Average Velocity

13. Speed or Velocity? • 186,282 mi. / s • 107 km / h North • 55 mi. / h • 1300 km / h East • 212 mi. / h

14. Practice • Which is a race car driver concerned with – speed or velocity? a drag racer? • The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. • Do both cars have the same speed? • Do both cars have the same velocity? • During certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed or a constant velocity? velocity [curved path] speed [going straight] yes no constant speed – if it were velocity, there would be a direction listed

15. More Practice • How might you estimate your speed if the speedometer in your car is broken? • Once more, explain the difference between speed and velocity to a partner. [various]