Problem:

Bir motorcu şehir sınırını geçtikten sonra doğu yönündeki bir kasabaya doğru 4 𝑚 𝑠!’ lik ivme ile hızlanmaya başlar. 𝑡 = 0 anında, motorcu

şehir sınırından 5𝑚 doğudadır ve doğu yönünde 15 𝑚 𝑠 sürate sahiptir;

a) motorcunun 𝑡 = 2𝑠’ deki hızını ve konumunu belirleyiniz.

b) Motorcunun sürati 25 𝑚 𝑠’ ye ulaştığında konumu ne olur belirleyiniz.

Problem:

Bir top yüksek bir binanın tepesinden 15 𝑚 𝑠 sürat ile yukarı doğru atılmaktadır. Top düşerken binaya çarpmadan

düşmeye devam eder ise;

a) Top atıldıktan 1𝑠 sonra hızı ve konumu ne olur?

b) Top atıldıktan 4𝑠 sonra hızı ve konumu ne olur?

c) Top atılış noktasından 5𝑚 yukarıda iken hızı nedir?

d) Top maksimum yüksekliğe eriştiği anda ivmesi nedir?

e) Top atıldıktan 3𝑠 sonra ivmesi nedir?

50 CHAPTER 2 Motion Along a Straight Line

Example 2.4 Constant-acceleration calculations

A motorcyclist heading east through a small town accelerates at aconstant after he leaves the city limits (Fig. 2.20). Attime he is 5.0 m east of the city-limits signpost, moving eastat (a) Find his position and velocity at (b) Where is he when his velocity is

SOLUTION

IDENTIFY and SET UP: The x-acceleration is constant, so we canuse the constant-acceleration equations. We take the signpost as theorigin of coordinates and choose the positive x-axis to pointeast (see Fig. 2.20, which is also a motion diagram). The knownvariables are the initial position and velocity, and

, and the acceleration, The unknowntarget variables in part (a) are the values of the position x and the x-velocity at the target variable in part (b) is the valueof x when vx = 25 m > s .

t = 2.0 s;vx

ax = 4.0 m > s2.v0x = 15 m > sx0 = 5.0 m

(x = 0)

25 m > s?t = 2.0 s.15 m > s.

t = 04.0 m > s2

Eq. (2.12) and the x-velocity at this time by using Eq. (2.8):

(b) We want to find the value of x when but wedon’t know the time when the motorcycle has this velocity. Table2.4 tells us that we should use Eq. (2.13), which involves x, , and

but does not involve t:

Solving for x and substituting the known values, we find

EVALUATE: You can check the result in part (b) by first using Eq. (2.8), to find the time at which which turns out to be t 2.5 s. You can then use Eq. (2.12),

, to solve for x. You should find ,the same answer as above. That’s the long way to solve the problem,though. The method we used in part (b) is much more efficient.

x = 55 mv0xt + 12 axt

2x = x0 +=

vx = 25 m>s,vx = v0x + axt,

= 5.0 m +125 m > s22 - 115 m > s22

214.0 m > s22 = 55 m

x = x0 +v 2

x - v 20x

2ax

v 2x = v 2

0x + 2ax1x - x02ax

vx

vx = 25 m > s,

= 15 m > s + 14.0 m > s2212.0 s2 = 23 m > s

vx = v0x + axt

= 43 m = 5.0 m + 115 m > s212.0 s2 + 1

2 14.0 m > s2212.0 s22 x = x0 + v0xt + 12 axt

2

vx

EXECUTE: (a) Since we know the values of , , and , Table2.4 tells us that we can find the position x at by using t = 2.0 s

axv0xx0

19651AWx

19651AWx

x (east)x 5 ?t 5 2.0 s

O

v0x 5 15 m/s vx 5 ?

ax 5 4.0 m/s2

x0 5 5.0 m t 5 0

OSAGE

2.20 A motorcyclist traveling with constant acceleration.

Problem-Solving Strategy 2.1 Motion with Constant Acceleration

IDENTIFY the relevant concepts: In most straight-line motion prob-lems, you can use the constant-acceleration equations (2.8), (2.12),(2.13), and (2.14). If you encounter a situation in which the accelera-tion isn’t constant, you’ll need a different approach (see Section 2.6).

SET UP the problem using the following steps:1. Read the problem carefully. Make a motion diagram showing

the location of the particle at the times of interest. Decidewhere to place the origin of coordinates and which axis direc-tion is positive. It’s often helpful to place the particle at the ori-gin at time then Remember that your choice ofthe positive axis direction automatically determines the posi-tive directions for x-velocity and x-acceleration. If x is positiveto the right of the origin, then and are also positive towardthe right.

2. Identify the physical quantities (times, positions, velocities, andaccelerations) that appear in Eqs. (2.8), (2.12), (2.13), and(2.14) and assign them appropriate symbols — x, and , or symbols related to those. Translate the prose intophysics: “When does the particle arrive at its highest point”means “What is the value of t when x has its maximum value?”In Example 2.4 below, “Where is the motorcyclist when hisvelocity is ” means “What is the value of x when

” Be alert for implicit information. For example,“A car sits at a stop light” usually means

3. Make a list of the quantities such as x, and t.Some of them will be known and some will be unknown.

ax,v0x,vx,x0,v0x = 0.

vx = 25 m > s?25 m > s?

ax

v0x,vx,x0,

axvx

x0 = 0.t = 0;

Write down the values of the known quantities, and decidewhich of the unknowns are the target variables. Make note ofthe absence of any of the quantities that appear in the fourconstant-acceleration equations.

4. Use Table 2.4 to identify the applicable equations. (These are oftenthe equations that don’t include any of the absent quantities thatyou identified in step 3.) Usually you’ll find a single equation thatcontains only one of the target variables. Sometimes you must findtwo equations, each containing the same two unknowns.

5. Sketch graphs corresponding to the applicable equations. The graph of Eq. (2.8) is a straight line with slope . The

graph of Eq. (2.12) is a parabola that’s concave up if ispositive and concave down if is negative.

6. On the basis of your accumulated experience with such prob-lems, and taking account of what your sketched graphs tell you,make any qualitative and quantitative predictions you can aboutthe solution.

EXECUTE the solution: If a single equation applies, solve it for thetarget variable, using symbols only; then substitute the known val-ues and calculate the value of the target variable. If you have twoequations in two unknowns, solve them simultaneously for the target variables.

EVALUATE your answer: Take a hard look at your results to seewhether they make sense. Are they within the general range of val-ues that you expected?

ax

axx-taxvx-t

Problem:

Bir binanın 8m yükseklikteki penceresinden 10 𝑚 𝑠 ilk sürat ile yatayla yatayın altında 20° açı yapacak şekilde bir taş fırlatılmıştır. Taş

binadan kaç metre uzakta yere çarpar?

Problem:

Bir festival oyununda, metal bir parayı uzaktaki bir tabak içerisine atmayı başardığınızda

oyuncak bir zürafa kazanmaktasınız. Tabak sizden yatay olarak 2,1𝑚 uzakta olan bir rafın

üzerindedir ve metal para elinizi 6,4𝑚 𝑠 sürat ile yatayla 60° açı yapacak şekilde terk

etmektedir. Bu atışın başarılı olduğunu kabul ederek;

a) Metal parayı attmış olduğunuz yükseklikten ölçüldüğünde tabağın bulunduğu

yüksekliği hesaplayınız.

b) Metal paranın tabağa çarpmadan hemen önceki hızını hesaplayınız.

Problem:

A bloğu 60𝑁 ağırlığındadır ve üzerinde durduğu yatay zeminle A bloğu arasındaki statik

sürtünme katsayısı 𝜇! = 0,25’ dir.

a) W ağırlığının 12𝑁 olduğu durumda sistem hareketsiz ve dengede ise, A bloğu üzerine

etki eden sürtünme kuvvetini belirleyiniz.

b) Sistemin hareketsiz ve dengede kalabileceği maksimum W ağırlığını belirleyiniz.

Problem:

𝑚! = 20𝑘𝑔 kütlesi ile 𝛼 = 53,1° eğimli yüzey arasındaki kinetik sürtünme katsayısı 𝜇! = 0,4’ dür.

Asılı 𝑚! kütlesinin, ilk hızsız serbest bırakıldıktan 3𝑠 sonra 12𝑚 alçalabilmesi için değeri ne

olmalıdır?