Linear Motion

1. Linear Motion Physics

2. Linear Motion Speed Velocity Acceleration Free Fall

3. Motion is Relative • All motion must be measured with respect to something. • A car driving at 35mph is moving at 35 mi/h with respect to the road. • Everything moves. Even things that appear to be at rest move. • The Earth, Sun, your desk… • All motion is relative.

4. When sitting on a chair, your speed is zero relative to the Earth but 30 km/s relative to the sun 100 km/h 98 km/h Question: What is the impact speed when a car moving at 100 km/h bumps into the rear of another car traveling in the same direction at 98 km/h?

5. Speed is how fast something is moving or the rate distance is covered. Speed is measured in distance/time m/s, km/h, mi/h There are 2 types of speed Instantaneous speed The speed of an object at a given time. In your car this is shown on your speedometer Average Speed Total distance/time Speed

6. Average Speed • Average speed is the whole distance covered divided by the total time of travel. • General definition: • Average speed = total distance covered/time interval • Distinguish between instantaneous speed and average speed: • On most trips, we experience a variety of speeds, so the average speed and instantaneous speed are often quite different. • Is a fine for speeding based on ones average speed or instantaneous speed?

7. Finding Average Speed • Example 1: If we travel 320 km in 4 hours, what is our average speed? If we drive at this average speed for 5 hours, how far will we go? • Answer: vavg = 320 km/4 h = 80 km/h. • d = vavgx time = 80 km/h x 5 h = 400 km. • Example 2: A plane flies 600 km away from its base at 200 km/h, then flies back to its base at 300 km/h. What is its average speed? • Answer: • total distance traveled, d = 2 x 600 km = 1200 km; • total time spent ( for the round trip), t = (600 km/200 km/h) + (600 km/300 km/h) = 3 h + 2 h = 5 h. • Average speed, vavg= d/t = 1200 km/5 h = 240 km/h. • Tip: start from the general definition for average speed!

8. Velocity • Velocity is speed in a given direction. • 70 mi/h is speed 70 mi/h north is velocity • The same equation can be used to calculate both • v = d/t • If something is moving at a constant velocity, it has constant speed and direction. – straight line path

9. 45 mi/h E Circle around the race track at 45 mi/h Question: which car is moving with a constant velocity? Constant speed? Why?

10. Acceleration • Acceleration is the rate at which velocity changes. • acceleration = Δv/t • Acceleration is measured in m/s2 • An object can be accelerated by changing its speed, direction, or both. • We have no deceleration, just positive and negative acceleration.

11. If the odometer in your car read 0 when you started and 35km half an hour later, what was your average speed? If a cheetah can maintain a speed of 25m/s for 10. min, how far will he travel? Avg speed = total d/t 35km/.5h = 70 km/h v = d/t 25m/s = d/10min 25m/s = d/600s 600s x 25 m/s = d 15000m = d Examples

12. A car goes from 10.0km/h to 45.0km/h in 3.00s. What is its acceleration? In 5.0 seconds, car A goes from 30.m/s to 39m/s. Car B goes from 0.0m/s to 9.0m/s. Which has greater acceleration? a = Δv/t a = (45km/h – 10km/h)/3s a = 11.7 km/h*s They both have the same acceleration. Δv = 9m/s for A and B t = 5s for A and B So a = 9m/s/5s a = 1.8 m/s2 for both. Examples 2

13. Acceleration Formulas Things to remember: vf = Final velocity vo = Initial velocity Upward movement = (+) for distance and acceleration Downward movement = (-) for distance and acceleration • a = vf – vo / t • d = ½ at2 • d = vot + ½ at2 • vf2 = vo2 + 2ad • vf = vo + g t • v = d/t

14. Acceleration Problems A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3.00 m/s2. The takeoff speed for this plane will be 65.0 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?

15. Acceleration on Galileo’s Inclined Planes • Galileo’s findings: • A ball rolls down an inclined plane with unchanging acceleration. • The greater the slope of the incline, the greater the acceleration of the ball. • If released from rest, the instantaneous speed of the ball at any given time = acceleration x time. • What is its acceleration if the incline is vertical?

16. When an object is dropped, does it accelerate? Yes, all falling objects experience acceleration due to gravity. An object acted on only by gravity is in free fall. Down = (+) velocity Up = (-) velocity Gravity accelerates all objects the same amount. Acceleration due to gravity = g = 9.8 m/s2 The instantaneous velocity of any free falling object can be found using the equn. v = gt or vf2 = vo2 + 2g d vf = vo + g t Free Fall

17. How fast? • An apple falls from a very tall tree. It falls for 3s. How fast is it moving after each second? • v = gt or v = at • v = (9.8m/s2)(1s) = 9.8 m/s • v = (9.8m/s2)(2s) = 19.6 m/s • v = (9.8m/s2)(3s) = 29.4m/s

18. How far? • To find how far something goes in a given time, we need to know its average velocity • Galileo’s finding from the inclined planes experiment: • The distance traveled by a uniformly accelerating object is proportional to the square of the time: Distance traveled = (1/2) x (acceleration) x (time2). • For a freely falling object, d = ½ gt2. • An object that starts at rest is going 9.8m/s after 1s of free fall. What is its avg. v? • (0m/s + 9.8m/s)/2 = 4.9m/s • How far then did it fall in that second? • 4.9m

19. Time (s) 0 1 2 3 4 5 6 Distance Fallen (m) 0 4.9 19.6 44.1 78.4 122.5 176.4 Free Fall Distance

20. Free Fall Distance • To calculate how far an object falls in a given time, we use the equation • d = ½gt2 • How far will a monster truck fall in 10s? • d =(1/2)(9.8m/s2)(10s)2 • d = (4.9m/s2)(100s2) = 490m • How far will a feather fall in that same time? (with no air resistance) • The same distance.