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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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2 years ago
Simplify this expression, you are y years old. Your sister is 3 years older than you. Your uncle is 4 times older than your sist
uysha [10]

Answer:The simplified expression that represents the uncle's age is

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Let y represent your age.

Your sister is 3 years older than you. This means that your sister's age is y + 3

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The simplified expression that represents your uncle's age would be

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8 0
3 years ago
The plot below shows the graphs of three functions, f, g, and h, all of which determine the population of three different cities
monitta

So, here we have an exponential function.

Remember that an exponential function has the form:

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So, given that the population of City A in 2000 was 40 thousand people and the population increased by 13% each year, we can say that

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For city B:

\begin{gathered} a=40 \\ b=1+\frac{16}{100}=1.16 \\ g(x)=40(1.16)^x \end{gathered}

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Answer:

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Step-by-step explanation:

Linear equations have the highest degree to be 1.

Therefore y=-x is linear.

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