Number of MCQ Ac guo saJl Il orc

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Maximum Overall Grade AS JI S pail dal

Marks of MCO Ass guo gall II ra

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Exam Duration - Ole! 54»

150 minutes 14 ale påle (yöl 95 A Physics Toolkit slat! JI J> - 1 ; = = a Slope = m = "0 _ ^V y=mx +b y=ax?+bx+c y=" REPRESENTING MOTION Spal 29-2 R=A+B = = if: m Ax | Xp Xi = Ae. Slop = da = T= E R=A-B AX = xy — Xi f i Ax Xf — Xi Xr — vt t X; = = c= f Li Average Speed = Vayg AF = | Accelerated motion | àe, ull aS JI -3 a,,, = slop = "= "- - AnUAlxajaS aJ oles | yx) Log dual aS yx) colas Vr— vitat Vy = v;+gt v? = v? -2a Ax vj = vi +2g Ay 1 1 1 1 Ax = vittz at Ay = vit+5 gt g=-9.81 m/s?

EI eaa FARW ee ooo e

EXAMPLE Problem 3

FINDING DISPLACEMENT FROM A VELOCITY-TIME GRAPH Th ity-time graph at the right shows the motion of an airplane of the airplane for At=10 s and for sa Let the positive direction be forward.

82 1 ANALYZE AND SKETCH THE PROBLEM 80 5 x c IE 78 * The time intervals begin at t — O.O s. = 76 KNOWN UNKNOWN 8 “ v=+75m/s Ax-? g 4 At=1.0s 72 At= 20s 0.

3.0 2 SOLVE FOR THE UNKNOWN

Use the relationship among displacement, velocity, and time interval

to find Ax during At — 1.0 s. dis Pla ceme 7 A «eo. — rw

bstiti = +75 = f b y - 1 9 ANO Substitute v m/s. = S. [ d ots: A ea ELT titut /s, At = 1.0 s. o

Use the same relationship to find Ax during At — 2.0 s. fov a t 220 a rea =7 5 X 2.9

= 160 O Substitute v= +75 m/s, At = 2.0 s.

Apply the equation of motion relating the final velocity of an object to its initial velocity, voblenis 5.6 uniform acceleration, and time (vf = vi + at) p T

Time (s)

s forward velocity increases from Answer:

time interval. What

6. The race car in the previous problem slows from

i to Ems over 3.0 s. What is its t t

5. A race car

Use appropriate significant figures to record answers from a mathematical operation, with the correct number of digits

8. Significant Figures Solve the following

y» Point jä Wd SIU oe vas NN problems, using the correct number of signifi-

Answer:

cant figures each time. @) eg 22. 22. â i | 40:d- 9.200 = 2:936. = 2:996 ..7]....... b. 4.75 E z 0.4168 M GW rí a sas y y y y y o a c. 139 cm x 2.3 cm

d. 1378 g9/03 m. M, KJ. VL 1 229.27. VIINI. Tn S9. GAU.

e. 1.6 km + 1.62 m + 1200 cm

AD OU O) MI = | WW = 1.6% 5 [boo

/ o | W a^ | LU a c — ie | LUST A3) JZ2MM 28 ceu» Y yM Y PLE a geal Ta

Figure 10 You can use a diagram or an equation to combine vectors. Analyze What is the sum of a vector 12 m north and a vector 8 m north? Displacement (x) ===> green

Example of Vector Addition Sam e d ire ck io) h dd

Origin g 3 z

— LLUIÜUL)IÍ

Examples of Vector Subtraction A

Origin 4kmeast — ; a

aa Gkmwes |

ResultantR 2 km west

Resultant R 3 km east

Apply the equation of motion, (xf = vavgt + xi) or (xf - xi = vavgt), in numerical problems to calculate the position or other physical quantities EXAMPLE Problem 4

POSITION The figure shows a mot ist travelii a straight road. After passi nt cyclist continues to travel at an and arrives at point C E is the of point C?

1 ANALYZE THE PROBLEM Choose a coordinate system with the origin at A.

KNOWN UNKNOWN

V= 12 m/s east nm | | | x,— 46 m east

t—30s

2 SOLVE FOR THE UNKNOWN Use magnitudes for the calculations.

Substitute v = 12 m/s, t = 3.0 s, and x, = 46 m.

3 EVALUATE THE ANSWER Are the units correct? Position is measured in meters.

Does the direction make sense? The motorcyclist is traveling east the entire time.

Classify physical quantities into vector and scalar quantities (distance, mass, displacement, rannassa the book speed, velocity, acceleration, force, work, energy, pressure)

Vectors and Scalars Scalars. Vectors

As you might imagine, there are many kinds of measurements and numbers used to represent or A v$ t ance ve lo C H F hs describe motion. If you needed to describe how far you ran, you might say that you ran 1.6 km. If

you needed to run to a specific location, you might say that you need to run 1.6 km north. Many Fe yn p re bu re Fo re e quantities in physics have both size, also called magnitude, A quantity that has N nt both magnitude and direction is called a vector. You can represent a vector with an arrow. The Fim e. uti: 9 length of the arrow represents the magnitude of the vector, and the direction of the arrow e

represents t tie direction of the vector. A quantity that is just a number Y a 2mm. $ fe e d d (5 Pl acevacv t

such as ce, ', time, or tet is called a scalar. In this textbook,

letters ‘ore represent vector quantities and regular letters to represent sei ym 5 acce le vo Y (ov

Apply the alternative equation of motion relating an object's final velocity to its initial velocity, its constant aceleration, problem 16 and its initial and final positions (v2f = v2i + 2a(xf - xi)) °

16. A golf ball rolls up a hill toward a miniature-golf Answer: hole. Assume the direction toward the hole is

positive. V. »

a. If the golf ball starts with a

and t a con D a of is its after 20st

3 What is the golf ball’s if the constant acceleration continues c. be the

Descri dme the golf ball in words - and with a motio ram.

Define a coordinate system and identify the origin, position, and distance in a coordinate system

Figure 9 The vectors x. and x, re nt positions. The vector An represents displacement from x, to x.

Describe the displacement from the lamppost to the cactus.

pn 2 Xp- H ed

dis Place rene

9 Describe the motion of an object if its velocity and acceleration are either in the same directions or opposite directions, hence state if an object is slowing down or speeding up

za EN ee en ee ee FN | | [e O O

Figure 2 The change in length of the velocity vectors on these EE cates whether the jogger is speeding up or slowing down.

i nya o e o .

S Perding up S I ow 9 down = = : con stan : ——— ———————————————————Á NEN o e NEN ed

as mentioned in the book 57

EN pole | om | KC

12. Position-Time and Velocity-Time Graphs run at a constant velocity of Answer: . Figure 10 shows the positions of both joggers at time

in the f their motion?

E p—————— Doom m | WA |

2. Use the v-t graph of the toy train in Figure 9 to answer these guestions. a. When is the train's speed constant? b. which time interval is the train's €. Mn s the train's acceleration most

3. Refer to Figure 9 to find the following time intervals.

a. 0.0sto5.0s b.

of the train during the

Figure 9 Time (s)

Answer:

Q, eee iem. D t6 PA bse mte Pe oun

azo-° -

BW ae uy Noe

Reading velocity-time graphs The motions of five runners are shown in Figure 6. Assume that the of Graphs are zero. Both graphs - Graph to the east shows motion with a

indicates a are

Graph C has a negative slope. It shows motion that _ Time (s) | |begins with a positive velocity, slows down, and then stops. This means the acceleration and the velocity are

Runners' Motion Graph

s £ 2 o o T >

at that time. It

Define displacement as the change in an object's position as mentioned in the book Define average velocity and average acceleration

The symbol Ax represents the change in position from the cactus to the lamppost. Because a erage velocity change in position is described and analyzed so often in physics, it has a special name. In An ci

is defined as the cl

physics, a change in position is called à displacement. Because displacement has both magnitude

and direction, it is a vector.

"iei

o. A The average acceleration of an object is «=O V velocita allt \e fati on interval divided by that time interval. Average acceleration is measured in meters per second per Cw l 2

(^ / $ 2 ) second (m/s/s), or simply meters per second squared X Posi ton

A = ev = VI t (m)

Lone AE

ble 1 and figure 11 Tp Me StePes 22 =

Table 1 Position v. Time LITETTITTJ [-9 Position (m) EMI LLLLI LL [111 T. I [1] ee | as Em eb 29] ^ 4251 40 See 19 [I] mm A d EH | 1 Time

Represent data in graphical form, draw the best fit line, and identify from the shape of the graph if the relationship between the variables is linear, quadratic or inverse

vd 1 Length of a Spring for

When the line of best fit is a straight line, as in Figure 15, there is a linear relationship between Different Masses €— : 8 = -— = P

the variables. In a linear relationship, the dependent variable varies linearly with the indepen- dent variable. The relationship can be written as the following equation.

— e

Slope The slope of a line is equal to the rise divided by the run, which also can be expressed as the vertical change divided by the horizontal change.

SloPe m= fie Re

yt Distance Ball Falls v. Time c ¥ 20 Relationship Between Speed

and Travel Time

x 5

dau

o Le. LL LLL Llc 04 08 12 16 20 O "35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 Time (s) Speed (km/h) is a quadratic relationship, represented by the equation Inverse relationships The graph in Figure 18 shows how the time it takes to travel 300 km below. A quadratic relationship exists when one variable varies as a car's speed increases. This is an example of an inverse relationship, represented by depends on the square of another. the equation below. An inverse relationship is a hyperbolic relationship in which one variable

depends on the inverse of the other variable.

Between Two Variables N nverse Relationship Between Tuo Vare las

[0-0] Xizo EXAMPLE Problem 4 DISP! IT An automobile el a traffic light turns green. will it have gone when î = a = U? 2a (^g -X x) 1 ANALYZE AND SKETCH THE PROBLEM

+e œ Sketch the situation. etch the situation o) S o & + Establish coordinate axes. Let the positive direction be to the right. = 8 1 e,

initial velocity, uniform acceleration, and time

* Draw a motion diagram.

KNOWN UNKNOWN

X = 0.00 m X=?

v, = 0.00 m/s —

iam Begin ee» ee > e LE

a =a = +3.5 m/s? a 2 SOLVE FOR THE UNKNOWN Use the relationship among velocity, acceleration, and displacement to find x.

Ja = Us + 20(x,— x)

v? r3 v2 X cb +25 m/s}? — (0.00 m/s] = 0.00 m + S Substitute x = 0.00 m, v, = +25 m/s, v, = 0.00 m/s, a = +3.5 m/s?. = +89m

3 EVALUATE THE ANSWER + Are the units correct? Position is measured in meters.

+ Do the signs make sense? The positive sign agrees with both the pictorial and physical models.

+ Is the magnitude realistic? The displacement is almost the length of a football field. The result is reasonable because 25 m/s (about 55 mph) is fast.

E Define and identify independent and dependent variables for a given data set as mentioned in the book BEEN

mass! SPring strekched

Independent and dependent variables A variable is any factor that might affect the behavior of an experimental setup. The factor that is a. ud an investigation

is the independent variable. In the experiment that gave the data in the independent variable. The n the independent variable is the + dependent variable. In this investigation, the amount the spring streched depended on the inde P end en de Pe n dent

mass, so the amount of stretch was the dependent variable.

the mass was

Interpret a position-time graph that represents the motion of a single object exile problem 2 Interpret a position-time graph that represents the motion of multiple objects pP

EXAMPLE Problem 2

INTERPRETING A GRAPH The graph to the right describes the motion of two runners moving along a straight path. The lines representing their motion are labeled A and B. When and where does runner B pass runner A?

1 ANALYZE THE PROBLEM Position v. Time Restate the questions. Y 5 Question 1: At

Question 2:

2 SOLVE FOR THE UNKNOWN Question 1 Examine the graph to find the intersection of the line representing the

motion of runner A with the line representing the motion of runner B. These lines intersect at time 45 s.

Position (m)

Question 2

Examine the graph to determine the position when the lines representing the motion of the runners intersect. The position of both runners is about 190 m from the origin.

Runner B passes runner A about 190 m beyond the origin, 45 s after A has Time(s)

passed the origin.