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3 years ago

14

5. A bus starting from rest accelerates in a straight line at a constant rate of 3m/s2 for 8s. Calculate the distance travelled

by the bus during this time interval.

1 answer:

mojhsa [17]3 years ago

8 0

Answer:

d = 96 meters

Explanation:

a = acceleration

t = time

d = distance

$d = \frac{1}{2} \times a \times {t}^{2}$

$d = \frac{1}{2} \times 3 \times {8}^{2}$

$d = 96$

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Aliya deposited half as much money in a savings account earning 1.9% simple interest as she invested in a money market account t

yanalaym [24]

Let <em>A</em> be the amount of money that Aliya deposited in the savings account. Since <em>A</em> is half as much as money as she invested in a money market account, then the amount that she invested in the market account is <em>2A.</em>

<em />

Express the interest that Aliya earned in terms of A. Set it equal to the amount of $297.60 and then solve for <em>A</em>.

Since the savings account gives 1.9% simple interest, the total amount of interest that she will earn from the savings account is 1.9% of A, which is equal to:

$\frac{1.9}{100}\times A$

Since the money market account gives 3.7% simple interest, the total amount of interest that she will earn from the money market account, is 3.7% of <em>2A</em>, which is equal to:

$\frac{3.7}{100}\times2A$

Add both interests in terms of A and simplify the expression:

$\begin{gathered} \frac{1.9}{100}\times A+\frac{3.7}{100}\times2A \\ =\frac{1.9}{100}\times A+\frac{7.4}{100}\times A \\ =(\frac{1.9}{100}+\frac{7.4}{100})\times A \\ =\frac{1.9+7.4}{100}\times A \\ =\frac{9.3}{100}\times A \end{gathered}$

The expression (9.3/100)*A represents the total interest after one year. Then:

$\begin{gathered} \frac{9.3}{100}\times A=297.60 \\ \Rightarrow A=\frac{100}{9.3}\times297.60 \\ \Rightarrow A=\frac{100\times297.60}{9.3} \\ \Rightarrow A=\frac{29760}{9.3} \\ \Rightarrow A=3200 \end{gathered}$

Use the value of <em>A</em> to find the amount that was invested in the money market account:

$2A=2\times3200=6400$

Therefore, Aliya deposited 3200 in a savings account and 6400 in a money market account.

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1 year ago

You have been asked to make a roller coaster more exciting. The owners want the speed at the bottom of the first hill doubled. H

qaws [65]

Answer:

The height will be 4 times.

Explanation:

Given that,

The speed at the bottom of the hill doubled.

We need to calculate the height

Using conservation of energy

$K.E_{t}+P.E_{t}=K.E_{b}+P.E_{b}$

$K.E_{b}=P.E_{t}$

$\dfrac{1}{2}mv^2=mgh$

$\dfrac{1}{2}m(4v^2)=mgh$

Therefore,

$P.E = mg(4h)$

Here, m and g are constant

Hence, The height will be 4 times.

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3 years ago

What does the term "speed" describe?

Blababa [14]

The cyclist who travels 20 kilometers per hour for 15 kilometers

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3 years ago

If i have a kinematic equation vf^2=vi^2-2*a(xf-xi), how can i solve for xi step by step

azamat

Answer:

Explanation:

$v_f^2 = v_i^2-2a(x_f-x_i)$

Subtract both sides by $v_i^2$ :

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Divide both sides by -2*a:

$\frac{v_i^2 - v_f^2}{2a} =x_f-x_i$

Add both sides by $x_i$ :

$x_i+\frac{v_i^2 - v_f^2}{2a} =x_f$

Subtract both sides by $\frac{v_i^2 - v_f^2}{2a}$ :

$x_i=x_f-\frac{v_i^2 - v_f^2}{2a}$

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3 years ago

A thin cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, wi

Vitek1552 [10]

Answer:

Explanation:

Let the velocity be v

Total energy at the bottom

= rotational + linear kinetic energy

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= 1/2 mv² +1/2 mv²

= mv²

mv² = mgh ( conservation of energy )

v² = gh

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