ass.2 2011 veh ausama ( u 5 ).final2

7/27/2019 Ass.2 2011 Veh Ausama ( U 5 ).Final2

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Sharjah Institute of TechnologyAssessment Activity Front Sheet

(This front sheet must be completed by the STUDENT where appropriate and included with the work submitted forassessment)

StudentsName:

AssessorsName:

AusamaI.hassan

Date Issued:14.11.2011

CompletionDate:

28.11.2011

Submitted on: / /

Qualification

BTEC National Diploma in Vehicle Technology ( Year-

1 )Unit No.: 5 Unit Title:

Applications Of Vehicle Science and

Mathematics

OutcomeNo. : 2

OutcomeTitle:

Be able to apply mathematical andstatistical methods to vehicle- relatedtasks

AssignmentNo. : 2 Assessmen

t Title:

Applications of mathematical andstatistical methods to vehicle relatedtasks

Part: 1 Of 1

In this assessment you will have opportunities to provide evidence against the followingcriteria. Indicate the page numbers where the evidence can be found

Criteriareference

To achieve the criteria the evidence must showthat the student is able to:

Tick ifmet

Pagenumbers

P 3Solve a linear equation by plotting a straight line graph ,using given

experimental data, and use it to deduce the gradient, intercept and

equation of the line for a vehicle-related task

P 4Factorize by extraction and grouping of a common factorexpressions with two, three and four terms respectively.

P5Use trigonometric ratios to solve two vehicle-related tasks.

M1Solve a pair of simultaneous linear equations in two unknowns.

M2Solve a quadratic equation by factorization and by the formulamethod.

Declaration

I certify that this assignment is my own work, written in my own words. Any otherpersons work included in my assignment is referenced / acknowledged.

CriteriaAchieved

P 1 P 2


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Students Name: Students Signature: Date:

Internal Verifiers approval to use with students

IVs Name:

Ashraf Senbel

IVs Signature: Date

BTEC National Diploma in Vehicle Technology ( Year-1 )

Unit 5: Applications of Vehicle Science and Mathematics.

Assignment 1 Applications of mathematical and statistical methods to

vehicle related tasks.

Task 1 (Pass P3)

A vehicle is accelerated at approximately constant rate from an initial speed of(10m/s) and the following

data were gathered :

Time, t (s) 2 4 6 8 10Speed, vm/s)

16 23 28 33 40

1. The relationship between speed and time is expected to be linear. Show that it is

so by plotting the speed against time.

2. Write the general equation of the straight line in terms of the gradient and

intercept with the vertical axes..

3. Calculate the gradient from the data given. What does it represent?

4. Calculate the intercept of the line with the vertical axis from the data given. What

does it represent?

5. Write the equation of the straight line for this particular case in terms of the

gradient and

the intercept of the line with the vertical axis.

Front Sheet


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Task 2 (Pass P4)

Factorize by extraction and grouping of a common factor from the following expressions (right-hand sides of

the equations below):

1.

The total energy of a vehicle with speed ,v

and height above ground level, mmassandh ,,,

(neglecting friction and air drag) is given by:

mghmvET +=2

2

1

2.

The total energy of a vehicle with speed ,v

and height above ground level, mmassandh ,,,

(with friction coefficient,

and neglecting air darg) is given by:

cot.2

1 2 mghmghmvETF +=


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3.

The total energy of two train carriages connected together moving with speed ,v

and at height above ground level, :.mod...,,,, 21 byelledbecanmmmassesandh

ghmvmghmvmET 22

21

2

12

1

2

1+++=

t=time of travel after attaining speed v and let go without further input power.

Task 3 (Pass P5)

A.

An engine has: Bore= 80mm

Stroke = 90mm

Number of Cylinders = 1

It is required to calculatethe Piston Displacement for this engine.

B.

Consider a classical steering trapezoid. If B=680 mm , mmlm 626=

mmrr 105= , calculate Ackerman angle , also find cos,,sin and using thecalculator, then

deduce the value of tan using the values obtained for cos,,sin and .


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Task4 (Merit M1

The linear stopping distance, )(s , in meters, covered by a vehicle with an initial speed )(u , in

meters per seconds, is given by:

2

2

1tauts F+=

(1)

Where:

t= time (in seconds) taken to cover the stopping distance.

)(FrictionalondeceleratiaF =

gaF =

sauvF

222+=


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0=v

gsu 20 2 =

g

us

2

2

=

Equation (1) reduces to:

22

)(2

1

2tgut

g

u

=

gtlet =....

22 )(2

12)(2 tggugtu =

22 )()(2 gtugtu =

222 = uu

The final equation which indirectly gives the time taken to cover the linear stopping distance (s),

in meters, covered by the vehicle with an initial speed )(u , in meters per seconds, is given

by the following quadratic equation:

...................(2)

Required to solve equation (2) to find the time (t) by:

1. Factorization

2. The formula.

Use only one value of (u) from the list below:

A. smu /50=

B. smu /80=

0222=+ uu


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C. smu /90=

D. smu /100=


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Piston Displacement = x (radius)2 x stroke x number of

cylinders

= 3.14

radius = bore/2

stroke = the distance from TDC to BDC

number of cylinders = the number of cylinders in the engine

Here is an Example:

This engine has: Bore= 80mm

Stroke = 90mm


Radius = Bore/2

= 80 2

= 40mm


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Piston Displacement = x (radius)2 x stroke x number of cylinders

= 3.14 x (40)2 x 90 x 1

= 3.14 x 1600mm x 90 x 1

= 452 160 mm3

You will notice that you answer is in mm3 . Engines are usually give a size of displacement in cm3

or commonly referred to as CC's. To convert your answer to CC's, divide your answer by 1000.

In this example, you would have 452 160mm3 1000 giving you an answer of 452.16 cm3 or

452.16 cc. This engine has a displacement of452.16 cm3 or 452.16 cc.

Often larger engines have their displacements measured in litres. To get this measurement, divide

you answer that is in cm3

or cc's by 1000. In this example, you would have 452.16cm3

1000giving you an answer of0.452 Litre or 0.452 L. This engine has a displacement of0.452 Litresor 0.452 L.

Here is One More Example:

This engine has: Bore= 87.5 mm

Stroke = 91.4 mm


Radius = Bore/2

= 87.5 2

= 43.75 mm

Piston Displacement = x (radius)2 x stroke x number of cylinders

= 3.14 x (43.75)2 x 91.4 x 2

= 3.14 x 1914mm x 91.4 x 2

= 1 098 656.5 mm3 or

= 1099 cm3 or

= 1.100 litres (L)


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This engine is a 1.100 litre two cylinder engine.

B.

Assessment Feedback Form(This feedback sheet must be completed by the ASSESSOR where appropriate)


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StudentsName:

Unit No.: 5Assessment Title:

Grading Criteria Achieved:

Unit Title:Applications Of Vehicle Science and

MathematicsOutcome No.: 2

OutcomeTitle:

AssignmentNo.: 2

Part: 1 of 1

Criteria ReferenceAssessment Criteria

Achieved

Evidence Comments/feedback

P 3

Solve a linear equation by plotting a straight

line graph ,using given experimental data,

and use it to deduce the gradient, interceptand equation of the line for a vehicle-related

task

Yes/No

P 4Factorize by extraction and grouping ofa common factor expressions with two,three and four terms respectively.

Yes/No

P5Use trigonometric ratios to solve twovehicle-related tasks.

Yes/No

M1Solve a pair of simultaneous linearequations in two unknowns.

Yes/No

M2Solve a quadratic equation byfactorization and by the formula

method.

Assessors General Comments:

Assessors Name: Ausama I.

Hassan

Signature: Date:

Students Comments:

Students Name: Signature: Date:

Feedback Sheet

P 1 P 2

Student's Work has been Internally Verified

IVs Name:

Ashraf Senbel

IVs Signature: Date:

ass.2 2011 veh ausama ( u 5 ).final2

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