EQ 1: What is motion? How do you know you are in motion?

Motion Motion is a change in the location of a body with respect to a reference point.

Distance is a measure of how far something has moved. SI Unit for length is the meter. Distance SI Unit for length is the meter.

DISPLACEMENT As an object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called the displacement of the object.

DISPLACEMENT Pause for a Cause: A man walks 20 miles from his house, and ends up 10 miles from where he started. His displacement is

DISPLACEMENT Displacement is not always equal to the total distance traveled. Displacement can be positive or negative.

Speed and Velocity Speed is a scalar quantity which refers to how fast an object is moving. (distance over time) Velocity is a vector quantity. It is speed in a given direction or rate of change of displacement. * Scalar-has magnitude Vector-magnitude with direction

Average Speed The average speed is given by: The unit for speed is meters (meters) per second (m/s), kilometers per hour (kph), centimeters per second, and miles per hour (mph).

Solve the Literal Equation S = d/t S = d/t

An MTR train takes 1267 seconds to travel a distance of 1557.9 m. Pause for a Cause An MTR train takes 1267 seconds to travel a distance of 1557.9 m. What is the trains speed? S = d/t d = 1557.9 m t = 1270 s S = 1.23 m/s S = d/t

Speed vs Velocity Speed and Velocity are similar in every way but, Velocity includes the speed of an object and the direction it is moving Speed vs Velocity

An MTR train travels south for 1267 seconds and covers 1557.9 meters. Pause for a Cause An MTR train travels south for 1267 seconds and covers 1557.9 meters. What is the trains velocity? V = d/t d = 1557.9 m t = 1270 s V = 1.23 m/s S = d/t

Pause for a Cause The train travels back north for 1400 seconds at 1.23 m/s How distance does the train travel? V = d/t d = vt v = 1.23 m/s t = 1400 s d = 1722 m S = d/t

Bell Ringer A bicyclist rides his bike at a velocity of 25m/s, before cycling up a hill. Peddling uphill his velocity decreases to 10m/s. What is his average velocity? Vavg. = Vi + Vf 2 Vavg. = 25m/s + 10m/s = 17.5m 2 s

Acceleration Acceleration is the rate of change in velocity. If a driver steps on his accelerator, his car moves faster—it accelerates (positive acceleration). If he steps on his brake, his car slows down—it decelerates (negative acceleration or retardation) . A change in velocity is given by the difference of the final velocity and the initial velocity. Thus, we have the equation: m/s This is expressed in s

Acceleration When the velocity of an object changes, the object is accelerating. A change in velocity can be either a change in fast something is moving, or a change in the direction it is moving. Acceleration is the change in velocity over time. m SI Unit for acceleration is expressed in s2

Three Simple Equations of Motion Average speed Acceleration

Three Not-So-Simple Equations Uniform Acceleration Vf = Vi + at ΔX = Vit + at2 2 Vf2 = Vi2 + 2aΔX

Three Not-So-Simple Equations Uniform Acceleration Vf = Vi + at Vf =final velocity Vi =initial velocity a=acceleration t=time taken

Uniform Acceleration Vf = Vi + at a = Vf - Vi  at = Vf - Vi t Vf = Vi + at

ΔX = Vit + at2 2 ΔX =displacement (distance from starting point) Vi =initial velocity t =time taken a=acceleration

ΔX = Vit + at2 2 Vavg = Vf + Vi V = ΔX  ΔX = Vt 2 t Vavg = Vf + Vi ΔX = Vt  2 ΔX = Vf + Vi t 2 ΔX =(Vi + Vi +at)t 2 2 Vf = Vi + at ΔX = Vf + Vi t  2 ΔX =(2Vi+at)t  ΔX = Vit + at2 2 2 2

Vf2 = Vi2 + 2aΔX Vf =final velocity Vi =initial velocity a=acceleration ΔX =displacement

Vf2 = Vi2 + 2aΔX Vavg = Vf + Vi V = ΔX  ΔX = Vt 2 t Vavg = Vf + Vi ΔX = Vt  2 ΔX = Vf + Vi t 2 ΔX = Vf + Vi t 2 a = Vf - Vi t aΔX = Vf + Vi t 2 Vf - Vi t aΔX = Vf2 – Vi2 2 2aΔX + Vi2 = Vf2 Vf2 = 2aΔX + Vi2

17). A body with an initial velocity of 8 m/s moves with a constant acceleration and travels 640 m in 40 seconds. Find its acceleration. ΔX = Vit + at2 2 ΔX = Vit + at2 2 640m = (8m/s)40s + a(402) ΔX =640m Vi =8m/s t =40s a=? 640m = 320m + a800 320m = a800s2 a = 0.4m/s2

17). A body with an initial velocity of 8 m/s moves with a constant acceleration and travels 640 m in 40 seconds. Find its acceleration. ΔX = Vit + at2 2 ΔX = Vit + at2  2ΔX = 2Vit + at2 2 ΔX =640m Vi =8m/s t =40s a=? 2ΔX = Vit + at2  2ΔX - 2Vit = at2 2ΔX - 2Vit = at2  2ΔX - 2Vit = a t2 2ΔX - 2Vit = a = 2(640) – 2(320) t2 402 a = 1280m - 640m 1600s2 a = 0.4m/s2

18) A box slides down an inclined plane with a uniform acceleration and attains a velocity of 27 m/s in 3 seconds from rest. Find the final velocity and distance moved in 6 seconds (initially at rest). a = Vf - Vi t V =27m/s Vi =0m/s t =3s 6s Vf =? a = Vf - Vi t a = 27m - 0 = 9m/s2 s * 3s 54m/s a = 9m/s2 Vf = Vi + at  Vf = 0 + 9m(6s) = 54m/s s2 ΔX = Vit + at2 2 ΔX = 9m(6s)2 = 162m s2 2 Vit = 0

19) A car has a uniformly accelerated motion of 5 m/s2 19) A car has a uniformly accelerated motion of 5 m/s2. Find the speed acquired and distance traveled in 4 seconds from rest. ΔX = Vit + at2 2 ΔX = Vit + at2 2 a = 5m/s2 t =4s ΔX =? V = ? Vit = 0 40m 20m/s ΔX = at2 2 ΔX = 5m(4s)2 = 40m s2 * 2 Vf = Vi + at Vf = 0 + 5m(4s) = 20m/s s2

20) Before leaving the ground an airplane traveling with constant acceleration makes a run on the runway of 1800 m in 12 seconds. Find a) acceleration b) speed at which it leaves the ground. ΔX = Vit + at2 2 ΔX = at2 2 a = ? t =12s ΔX = 1800 V = ? Vit = 0 a = 2ΔX t2 a = 2(1800) = 25m/s2 122 Vf = 25(12) = 300m/s Vf = Vi + at

21) A marble is dropped from a bridge and strikes the water in 5 seconds. Calculate the speed with which it strikes and the height of the bridge. (hint: The acceleration of gravity is 9.8m/s2) ΔX = Vit + at2 2 a = 9.8m/s2 t = 5s ΔX = ? V = ? Vit = 0 ΔX = at2 2 ΔX = 9.8(5s)2 = 122.5m 2 Vf = Vi + at Vf = 9.8(5) = 49m/s

22) A car starts from rest and accelerates uniformly to a velocity of 80 ft/s after traveling 250 ft. Find its acceleration. Vf2 = Vi2 + 2aX a = ? Vi = 0 ΔX = 250 V = 80 ft/s Vf2 = 2aX Vi = 0 Vf2 = 2aX a = Vf2 2X a = (80)2 = 12.8m/s2 2(250)

23) What velocity is attained by an object which is accelerated at 0 23) What velocity is attained by an object which is accelerated at 0.30 m/s2 for a distance of 50 m with a starting velocity of 0.0 m/s? Vf2 = Vi2 + 2aX a = 0.30 m/s2 Vi = 0 ΔX = 50 V = ? Vf2 = 2aX Vi = 0 Vf2 = 2aX Vf = √2aX Vf = √2(0.30)(50) = 5.5m/s

Graphing Constant Acceleration cccccc

Study Guide 1. The distance traveled by an object divided by the time it takes to travel that distance is called Study Guide

Study Guide 2. In order to determine speed, you must know Study Guide

Study Guide 4. The difference between speed and velocity is that velocity includes Study Guide

Study Guide 5. An airplane is flying at 635 km per hour at an altitude of 35 000 m. It is currently over Kansas and is approximately 16 minutes ahead of its scheduled arrival time. What is its velocity? Study Guide

Study Guide 6. Acceleration is defined as the change in velocity divided by Study Guide

Study Guide 7. The SI unit for acceleration is Study Guide

Study Guide 8. On a velocity-time graph, a line with a negative slope indicates that the object is Study Guide

Study Guide 9. A car moved 20 km to the South. What is its displacement? Study Guide

Study Guide 10. A car moved 20 km East and 80 km West. Draw a diagram and determine the distance? Study Guide

Study Guide 11. A car moved 120 km East and 180 km West. Draw a diagram and determine the displacement? Study Guide

Study Guide 12. What is the average speed of a car that traveled 450.0 miles in 7.2 hours? Study Guide

Study Guide 13. How much time would it take for the sound of thunder to travel 50 meters if sound travels at a speed of 33 m/sec? Study Guide

Study Guide 14. How much time would it take for an airplane to reach its destination if it traveled at an average speed of 500 miles/hour for a distance of 5,000 kilometers if there is 1.6km in 1 mile? Study Guide

Study Guide 15. How far can a person run in 45 minutes if he or she runs at an average speed of 32 km/hr? (HINT: Remember to convert minutes to hours.) Study Guide

Study Guide 16. A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in 15 minutes? Study Guide

Study Guide 17. A body with an initial velocity of 8 m/s moves with a constant acceleration and travels 640 m in 40 seconds. Find its acceleration. Δx = Vit + at2 2 Study Guide

Study Guide 18. A car has a uniformly accelerated motion of 5 m/s2. Find the speed acquired and distance traveled in 4 seconds from rest. Δx = Vit + at2 Vf = Vi + at 2 Study Guide

Study Guide 19. A car starts from rest and accelerates uniformly to a velocity of 80 ft/s after traveling 250 ft. Find its acceleration. Vf2 = Vi2 + 2aX Study Guide

Study Guide 20. What velocity is attained by an object which is accelerated at 0.30 m/s2 for a distance of 50 m with a starting velocity of 0.0 m/s? Vf2 = Vi2 + 2aX Study Guide