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IgorLugansk [536]
3 years ago
12

Analysis of an accident scene indicates a car was traveling at a velocity of 69.5 mph (31.1 m/s) along the positive x-axis at th

e instant the brakes were applied and then traveled a distance of 115 m before hitting an obstacle at a velocity of 5.20 m/s. Determine the car's acceleration a (assumed constant) and the time t between applying the brakes and hitting the obstacle. (Assume the car is moving in the positive direction. Indicate the direction with the sign of your answer.)
Mathematics
1 answer:
STatiana [176]3 years ago
7 0

We can find the acceleration via

{v_f}^2-{v_i}^2=2a\Delta x

We have

\left(5.20\dfrac{\rm m}{\rm s}\right)^2-\left(31.1\dfrac{\rm m}{\rm s}\right)^2=2a(115\,\mathrm m)

\implies\boxed{a=-4.09\dfrac{\rm m}{\mathrm s^2}}

Then by definition of average acceleration,

a_{\rm ave}=\dfrac{v_f-v_i}t

so that

-4.09\dfrac{\rm m}{\mathrm s^2}=\dfrac{5.20\frac{\rm m}{\rm s}-31.1\frac{\rm m}{\rm s}}t

\implies\boxed{t=6.33\,\mathrm s}

We alternatively could have found the time without knowing the acceleration. Since acceleration is constant, the average velocity is

v_{\rm ave}=\dfrac{x_f-x_i}t=\dfrac{v_f+v_i}2

Then

\dfrac{115\,\rm m}t=\dfrac{5.20\frac{\rm m}{\rm s}+31.1\frac{\rm m}{\rm s}}2

\implies\boxed{t=6.33\,\mathrm s}

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Hunter started with the following model to show the problem 1.45 : 5. w 3 To complete the division model of 1.45 = 5, how many h
Cloud [144]

Each division set gives the outcome of the operation 1.45 ÷ 5 which is 0.29.

  • The number of hundredths in each division set is <u>D. 9</u>

Reasons:

The given Hunter's model consists of the following

One 10 × 10 number block

Four sets of a column of 10 cubes

Five individual cube pieces

Therefore;

In 1.45, we have;

1 unit

4 tenths

5 hundredths

Which gives;

Each single cube can be used to represent a hundredth in 0.05

One cube = 0.01

Each set of 10 cubes represents a tenth in 0.4

Each block of 10 by 10 can be used to represent the unit; 1

Dividing each of the 10 × 10 can be divided to sets of 20 blocks with a value of 0.2 each

The 4 sets of 10s can be divided by 5 to give sets of 8 with a value of 0.08

The 5 cubes divided 5 gives five cubes with each cube having a value of 0.01.

Therefore;

The value of each division set is 0.2 + 0.08 + 0.01 = 0.29

The number of hundredths in 0.29 = 9

The number of hundredths in each division set is therefore; <u>D. 9</u>

Learn more about number place value here:

brainly.com/question/184672

5 0
2 years ago
Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit
Phantasy [73]

Answer:

y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

7 0
2 years ago
Elena is playing a dice game with her father. She will win if she DOES NOT roll a 1, 3, or 6. Find the probability that Elana wi
EleoNora [17]

Answer:

The probability that she was on her next roll is 1/2

Step-by-step explanation:

If she does not roll 1,3 or 6, she wins

So if she rolls 2,4 and 6 , she wins

The probability of rolling each is 1/6 each

So the probability of rolling any of the three will be:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

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2 years ago
Factor the expression.
valentinak56 [21]
It is (d+5)(d+5) because 5•5 is 25 and 5+5 is 10
4 0
3 years ago
What does 4 5/8 - 1 2/5 equal?
mihalych1998 [28]

4 \frac{5}{8}  - 1 \frac{2}{5}  \\  \\  \frac{37}{8}   -  \frac{7}{5}  \\  \\  \frac{185}{40}  -   \frac{56}{40}   =  \frac{185 - 56}{40}  \\  \\  =  \frac{129}{40}  = 3.225 = 3 \frac{9}{40}

I hope I helped you^_^

8 0
2 years ago
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