2. Notes on Motion III How Fast, How Far & How Long vdt

3. How Far? Distance (d) How Far you travel to get from one place to another. To get to the store go 2-miles east, turn right and go 3-miles south. How far will you travel to the store? 2 + 3 = 5-miles !!!!!

4. How Far? Units for distance are: English System Miles (mi), Yards (yds), Feet (ft), Inches (in) Metric System Kilometers (km), Meters (m), Centimeters (cm) In science the most common unit is: METERS

5. How Fast? Speed (v) The rate in which distance is covered. How fast distance is covered. Distance divided by time. Velocity (v) Speed with direction. It is also how fast, but it includes what direction. If you are traveling north at 65-mph. Your speed is : Your direction is : Your velocity is : 65-mph North 65-mph North

6. How Fast? Average Speed (v avg ) Total distance traveled divided by the total time to travel that distance. Average Speed is over a time interval. Instantaneous Speed (v) How fast distance is being covered at a specific moment in time. Your speedometer measures instantaneous speed.

7. How Fast? Constant Speed (v) When the speed of an object doesn’t change. Constant Velocity (v) When the neither the speed nor the direction of an object change. Can you have a constant velocity but not have a constant speed? NO!!!!!!! Can you have a constant speed but not have a constant velocity? Yes!!!!!!!

8. How Fast? Units for speed and velocity: English System Miles per Hour (mph), Feet per Second (ft/s) Metric System Kilometers per Hour (kph or km/hr), Meters per Second (m/s) In science the most common unit is: m/s

9. How Long? Time (t) Units: Centuries, Years (yr), Hours (hr), Minutes (min), Seconds (s or sec) In science the most common unit is: Seconds (s or sec)

10. Solving Problems with Velocity and Speed In general the equation that relates the speed (or velocity) of an object to the distance it travels and the time it takes is: With this equation, we can find the speed of an object if we know distance and time. But ….. What if we want to find distance from speed and time?

11. Solving Problems with Velocity and Speed If we need to find the distance from speed and time, we use algebra to solve for d: If we need to find the time from distance and speed we use algebra to solve for t:

12. Solving Problems with Velocity and Speed We can use a triangle to help us remember these formulas. First draw a triangle like this. The d is on top, so it goes in the top space. d vt Next use the formula to fill in the triangle. The v is on the left, so it goes in the left space. The t is in the bottom right, so it goes in the bottom right space. With this triangle you can get any of the three formulas you need!!!!

13. Solving Problems with Velocity and Speed d vt If you need to find d, cover d. Since v & t are next to each other, multiply them.

14. Solving Problems with Velocity and Speed d vt If you need to find v, cover v. Since d is on top of t, divide them.

15. Solving Problems with Velocity and Speed d vt If you need to find t, cover t. Since d is on top of v, divide them.

16. Solving Problems with Velocity and Speed d vt Example Problem 1: A runner finishes the 100-m dash in 9.4-s. What is the average speed of the runner during the race? Know: d = 100-m t = 9.4-s Find: v = ? Formula: Solve:

17. Solving Problems with Velocity and Speed d vt Example Problem 2: A car travels with a constant velocity north of 45- m/s (100-mph). How far will the car travel in 300-s (5 minutes)? Know: v = 45-m/s t = 300-s Find: d = ? Formula: Solve:

18. Solving Problems with Velocity and Speed d vt Example Problem 3: The circumference of the Earth is approximately 40,000-km. How long would it take you to drive this distance at 320-km/hr? Know: d = 40,000-km v = 320-km/hr Find: t = ? Formula: Solve: