kinematics ust

8/10/2019 Kinematics Ust

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Study of motion of bodies withoutregard to the forces acting on the body.


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Has mass, but its dimensions arenegligible or unimportant in theproblem being investigated.

A system of particles that remain atfixed distances from each other with no

relative translation or rotation amongthem.
http://localhost/var/www/apps/conversion/tmp/scratch_6/DisplaceDistance.html


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Differentiate distance and displacement .

a scalar quantity, the total path

covered by an object in motion.

a vector quantity, theshortest distance from the initial to the finalposition of an object.
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How do wedescribe themotion of

objects?


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A scalar quantityA measure of how fast anobject movesSpeed = distance / time


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=the speed of an object at any one instant

= measured by the speedometer


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The measure of the total distance traveled at a givenperiod of time.


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A vector quantity Rate of how an object changes its

position Used to describe speed and direction


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A vector quantity

Rate at which object changes its velocity


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change its speed Change its direction Change both speed and direction


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.

velocity ischanging by aconstant amounteach second


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Position vs time graphVelocity vs time graphAcceleration vs time graph


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1. What is the average speed of a cheetah that

sprints 100 m in 4 s? How about if it sprints 50m in 2 s?

2. If a car moves with an average speed of 60km/h for an hour, it will travel a distance of 60km.

a. How far would it travel if it moved at thisrate for 4h.

b. for 10 h?


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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/hto 65 km/h while a bicycle goes from rest to 5km/h. Which undergoes the greateracceleration? What is the acceleration of eachvehicle?


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1. A girl moves at a constant speed in a constantdirection. Say the same sentence in fewerwords.

2. The speedometer of a car moving to the east reads100 km/h. It passes another car that moves to the

west at 100 km/ h. Do both cars have the samespeed? 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 thisindicate a constant speed? A constant velocity?


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Summary of Formulas:

2

2

1

at t vd o

at vv o

ad vv 2202


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2

o f vvv

t vvd o

2


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SAMPLE PROBLEMS:

1. A sprinter is able to produce an acceleration of8.0 m/s 2 for the first 0.75 s of a race. Calculatethe velocity of the sprinter at the end of the first0.75 s?

2. Now suppose that the sprinter continues to runat 6.0 m/s until the end of the race. Aftercrossing the finish line the sprinter deceleratesat 2.0 m/s 2 . How long will it take her to stop?


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3. If a freight train can accelerate at 0.050 m/s 2, how farmust 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 accelerationtrauma incident (sudden stop) if the magnitude of the

acceleration is less than 250 m/s2.

If you are in a caraccident with an initial speed of 105 km/h and arestopped by an airbag that inflates from the dashboard,over what distance must the airbag stop you for you tosurvive the crash?


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SAMPLE PROBLEMS:

5 . An engineer is designing the runway for anairport. Of the planes which will use the airport,the lowest acceleration rate is likely to be 3m/s 2. The takeoff speed for this plane will be 65

m/s. Assuming this minimum acceleration, whatis 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 travelin this time? Assume constant acceleration.


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SEATWORK:

1. How long will it take a car to acceleratefrom 10m/s to 13m/s if it produces anacceleration of 3m/s 2 ?

2. How long will it take a car to cover adistance of 100 m if it accelerates fromrest at a rate of 4.0 m/s 2 ?


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SEATWORK:

3. How long will it take a car to cover a distanceof 250 m if it accelerates from rest at a rate of4.0 m/s 2 ?

4. A dolphin decelerates for 2.0 s from an initialspeed of 7.5 m/s in order to take a look at adolphin of the opposite sex. Calculate thedolphins final speed if the deceleration had amagnitude of 1.5 m/s 2 .


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SEATWORK:

5. An ice skater decelerates for 5.0 s to a finalspeed of 12 m/s. If the deceleration was at arate of 1.5 m/s 2 . What is the skaters initialspeed?


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CHALLENGE PROBLEM:

A car 3.5 in length and traveling at a constant speedof 20 m/s is approaching an intersection. The width ofthe intersection is 20m. The light turns yellow when

the front of the car is 50m from the beginning of theintersection. If the driver steps on the brake, the carwill slow at -3.8 m/s 2 . If the driver instead steps onthe gas pedal, the car will accelerate at 2.3m/s 2 . Thelight will be yellow for 3.0s. Ignore the reaction timeof the driver. To avoid being in the intersection whilethe light is red, should the driver hit the brake pedalor the gas pedal?


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CHALLENGE PROBLEM:

Two cars are 20 m apart. Car 1 is initially at restand car 2 is moving at a speed of 19m/s to theleft. The first car started to accelerate at 2m/s 2 to the right and car 2 continues to move at aconstant velocity, when will the two cars passeach other?


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CHALLENGE PROBLEM:

Two cars are 50 m apart. Car 1 is travelling at12 m/s to the left while car 2 is travelling at 10m/s to the right. If both cars accelerate at 2m/s 2 , when will they pass each other?


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ROAD SAFETY

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


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ROAD SAFETY

Ref: http://www.rotr.ie/rules-for-driving/speed-limits/speed-limits_2-second-


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NO SPEED LIMIT!


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An object falls underthe influence ofgravity alone

It is not affected by

air resistance


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Summary of Formulas:

2

2

1

gt t vd o

gt vv o

gd vv 2202


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v = gt


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d = (1/2) gt 2


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THE VANISHING COIN


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Free- fall

- Happens if the only force acting on the object isthe gravitational force

d = (1/2) gt 2

t =


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d = 1.5 cm or 0.015 m g = 9.8 m/s 2

Average reaction time of a person = 0.16 s

t =

t = 0.055s


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1. 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 fallingobject 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 itsvelocity before hitting the ground?


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3. A properly motivated kangaroo can jump over anobject 2.5 m high. A) Calculate its speed when it leftthe ground. B) Calculate its speed when it returns tothe ground.

4. A child throws a ball straight down off the balconyof an apartment building at a speed of 7.5 m/s. a)Calculate the position and the velocity of the ball 1and 2 s later. B) Make same calculations if the ball is

thrown straight up.


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5. A rock is thrown straight up with an initial speed of10 m/s. a) What distance does the rock rise above itspoint of release? b) How long does it take the rock toreach its highest point?

6. A stone is thrown vertically upward with a speed of12 m/s from the edge of a cliff 75 m high. A) Howmuch later does it reach the bottom of the cliff? Whatis its speed just before hitting the bottom? What is

the total distance travelled?


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7. A youngster throws a rock from a bridge into theriver 50 m below. The rock has a speed of 15m/swhen it leaves the youngsters hand.How much laterdoes it strike the water? Calculate the velocity of therock when it strikes the water a) if it is thrown straight

upward ; b) if its is thrown straight downward.


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Seatwork

1. A boulder is ejected straight up out of a volcano ata speed of 80 m/s. a) To what maximum height will itrise 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 therock to reach the bottom? B) calculate the position ofthe rock 1,2 and 3 s after its release.


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3. A rock is thrown from the rooftop 10 m from theground. It is thrown with an initial velocity of 12m/s.How much later does it strike the water? Calculatethe velocity of the rock when it strikes the water a) ifit is thrown straight upward ; b) if its is thrown

straight downward.

4. If a rock is dropped from a high cliff, how fast will itbe going when it has fallen 100m?b) How long will it

take to fall this distance?


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CHALLENGE PROBLEM:

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


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THANK YOU.


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