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KINEMATICS A branch of Mechanics which describes the motion of objects using words, diagrams, numbers, graphs, and equationsKINEMATICS

Study of motion of bodies without regard to the forces acting on the body.

ParticlesHas mass, but its dimensions are negligible or unimportant in the problem being investigated.Rigid bodyA system of particles that remain at fixed distances from each other with no relative translation or rotation among them. Differentiate distance and displacement. Distance a scalar quantity, the total path covered by an object in motion.

Displacement a vector quantity, the shortest distance from the initial to the final position of an object. SpeedA scalar quantityA measure of how fast an object movesSpeed = distance / timeInstantaneous speed=the speed of an object at any one instant

= measured by the speedometer

Average speed

The measure of the total distance traveled at a given period of time.

Velocity A vector quantity Rate of how an object changes its position Used to describe speed and direction

Acceleration

A vector quantity

Rate at which object changes its velocityHow to accelerate an object change its speed Change its direction Change both speed and directionConstant Acceleration.

velocity is changing by a constant amount each secondAcceleration

Acceleration

Positive Acceleration

Negative Acceleration

Describing motion using vector diagrams

Describing motion using Graphs Position vs time graphVelocity vs time graphAcceleration vs time graphGraph Interpretation

PROBLEM SOLVINGWhat is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s?

2. 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 4h.b. for 10 h?

3. A particular car can go from rest to 90 km/h in 10 s. What is its acceleration?

4. In 2.5 s a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the greater acceleration? What is the acceleration of each vehicle?QuestionsA girl moves at a constant speed in a constant direction. Say the same sentence in fewer words.

2. 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 they have the same velocity?

3. During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

Uniformly Accelerated MotionSummary of Formulas:

SAMPLE PROBLEMS:A sprinter is able to produce an acceleration of 8.0 m/s2 for the first 0.75 s of a race. Calculate the velocity of the sprinter at the end of the first 0.75 s?

Now suppose that the sprinter continues to run at 6.0 m/s until the end of the race. After crossing the finish line the sprinter decelerates at 2.0 m/s2 . How long will it take her to stop?3. If a freight train can accelerate at 0.050 m/s2, how far must it travel to increase its speed from 2.0 to 8.0 m/s? B) How long will it take the train to accomplish this?

4. The human body can survive a negative acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2. If you are in a car accident with an initial speed of 105 km/h and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

SAMPLE PROBLEMS:5 . An engineer is designing the runway for an airport. Of the planes which will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?

6. A car accelerates from 12 m/s to 25 m/s in 6s. What was its acceleration? How far did it travel in this time? Assume constant acceleration.

QuestionsA girl moves at a constant speed in a constant direction. Say the same sentence in fewer words.

2. 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 they have the same velocity?

3. During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity? SEATWORK:1. How long will it take a car to accelerate from 10m/s to 13m/s if it produces an acceleration of 3m/s2 ?

2. How long will it take a car to cover a distance of 100 m if it accelerates from rest at a rate of 4.0 m/s2 ?

SEATWORK:3. How long will it take a car to cover a distance of 250 m if it accelerates from rest at a rate of 4.0 m/s2 ?

4. A dolphin decelerates for 2.0 s from an initial speed of 7.5 m/s in order to take a look at a dolphin of the opposite sex. Calculate the dolphins final speed if the deceleration had a magnitude of 1.5 m/s2 .

SEATWORK:5. An ice skater decelerates for 5.0 s to a final speed of 12 m/s. If the deceleration was at a rate of 1.5 m/s2 . What is the skaters initial speed?

CHALLENGE PROBLEM:

A car 3.5 in length and traveling at a constant speed of 20 m/s is approaching an intersection. The width of the intersection is 20m. The light turns yellow when the front of the car is 50m from the beginning of the intersection. If the driver steps on the brake, the car will slow at -3.8 m/s2 . If the driver instead steps on the gas pedal, the car will accelerate at 2.3m/s2 . The light will be yellow for 3.0s. Ignore the reaction time of the driver. To avoid being in the intersection while the light is red, should the driver hit the brake pedal or the gas pedal?CHALLENGE PROBLEM:

Two cars are 20 m apart. Car 1 is initially at rest and car 2 is moving at a speed of 19m/s to the left. The first car started to accelerate at 2m/s2 to the right and car 2 continues to move at a constant velocity, when will the two cars pass each other?CHALLENGE PROBLEM:

Two cars are 50 m apart. Car 1 is travelling at 12 m/s to the left while car 2 is travelling at 10 m/s to the right. If both cars accelerate at 2 m/s2 , when will they pass each other?ROAD SAFETY

Ref: http://users.tpg.com.au/users/mpaine/speed.html#speedcrash

ROAD SAFETY

Ref: http://www.rotr.ie/rules-for-driving/speed-limits/speed-limits_2-second-NO SPEED LIMIT!

Free fall

An object falls under the influence of gravity alone

It is not affected by air resistanceFree fall

Acceleration due to gravity = 9.8 m/s2Free-fall equationsSummary of Formulas:

How fast an object fallsv = gtv = velocityg= acceleration due to gravityt = timeHow fard = (1/2) gt2d= distanceg= acceleration due to gravityt = timeTHE VANISHING COINFree- fall- Happens if the only force acting on the object is the gravitational force

d = (1/2) gt2

t =

d = 1.5 cm or 0.015 mg = 9.8 m/s2

Average reaction time of a person = 0.16 st =

t = 0.055s1. A cat steps off a ledge and drops to the ground in second.

a. What is its speed on striking the ground?b. How high is the ledge from the ground?

2. What is the velocity acquired by a freely falling object 5s after being dropped from a rest position? What is it 6s after? If it has reached the ground after 10s, from what height was it dropped? What is its velocity before hitting the ground?3. A properly motivated kangaroo can jump over an object 2.5 m high. A) Calculate its speed when it left the ground. B) Calculate its speed when it returns to the ground.

4. A child throws a ball straight down off the balcony of an apartment building at a speed of 7.5 m/s. a) Calculate the position and the velocity of the ball 1 and 2 s later. B) Make same calculations if the ball is thrown straight up. 5. A rock is thrown straight up with an initial speed of 10 m/s. a) What distance does the rock rise above its point of release? b) How long does it take the rock to reach its highest point?

6. A stone is thrown vertically upward with a speed of 12 m/s from the edge of a cliff 75 m high. A) How much later does it reach the bottom of the cliff? What is its speed just before hitting the bottom? What is the total distance travelled? 7. A youngster throws a rock from a bridge into the river 50 m below. The rock has a speed of 15m/s when it leaves the youngsters hand.How much later does it strike the water? Calculate the velocity of the rock when it strikes the water a) if it is thrown straight upward ; b) if its is thrown straight downward.

Seatwork

1. A boulder is ejected straight up out of a volcano at a speed of 80 m/s. a) To what maximum height will it rise above the point where it was ejected?

2. A rock is dropped into a 60.0 m deep well. A) Neglecting air resistance, how long will it take the rock to reach the bottom? B) calculate the position of the rock 1,2 and 3 s after its release. 3. A rock is thrown from the rooftop 10 m from the ground. It is thrown with an initial velocity of 12m/s. How much later does it strike the water? Calculate the velocity of the rock when it strikes the water a) if it is thrown straight upward ; b) if its is thrown straight downward.

4. If a rock is dropped from a high cliff, how fast will it be going when it has fallen 100m?b) How long will it take to fall this distance? CHALLENGE PROBLEM:

A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 3.4 s later. If the speed of sound is 340m/s, how high is the cliff?