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konstantin123 [22]
4 years ago
12

उक्त समयमा बसले कति दुरी पार गर्दछ ? Abusstarts from

Mathematics
1 answer:
SOVA2 [1]4 years ago
4 0

Answer:

<em>The magnitude of the velocity will be 60 m/s.</em>

<em>The distance covered is 3,600 m</em>

Step-by-step explanation:

<u>Constant Acceleration Motion</u>

It's known as a type of motion in which the velocity of an object changes by an equal amount in every equal period of time.

If a is the constant acceleration, vo is the initial speed, vf the final speed, and t the time, the following relation applies:

v_f=v_o+at

The distance traveled by the object is calculated as:

\displaystyle x=v_o.t+\frac{a.t^2}{2}

The bus starts from rest, i.e. vo=0, the acceleration is a=0.5 m/s^2. The magnitude of the velocity at t=2 minutes = 120 seconds is:

v_f=0+0.5\cdot 120=60 \ m/s

The magnitude of the velocity will be 60 m/s.

The distance covered during that time is:

\displaystyle x=0+\frac{0.5\cdot 120^2}{2}

\displaystyle x=\frac{7,200}{2}

x = 3,600 m

The distance covered is 3,600 m

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we have that

300 + 150 + 75 +...

Let

a1=300\\ a2=150\\ a3=75

we know that

\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50

\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50

so

a(n+1)=an*0.50

Is a geometric sequence

Find the value of a4

a(4)=a3*0.50

a(4)=75*0.50

a(4)=37.5

Find the value of a5

a(5)=a4*0.50

a(5)=37.5*0.50

a(5)=18.75

Find S5

S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25

therefore

the answer is

581.25

Alternative Method

Applying the formula

S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25

therefore

the answer is

581.25

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