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forsale [732]
2 years ago
12

A cyclist rides her bike at a rate of 2 meters per second. What is this rate in kilometers per hour? How many kilometers will th

e cyclist travel in 3 hours? Do not round your answers.
Mathematics
1 answer:
Oksanka [162]2 years ago
8 0

The speed v is 12 m/s.

 

You need to convert the seconds to hours  and meters to kilometers:

 

3600s = 1 hr

 

If you divide 3600 on both sides you will get

 

1 s = (1/3600) hr

 

 

1000m = 1 km

 

If you divide 1000 on both sides you will also get

 

1 m = (1/1000) km

 

 

v = [(12/1000) km] / [(1/3600) hr]

 

v = [(12*3600)/1000] km/hr

 

v = 216/5  km/hr

 

 

The distance in 4 hours is

 

d = [(216/5) km/hr] * 4hr

 

d = 864.50 km

This is why your answer should be 12 m/s

Hope this helps!! - Queenb369

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Given the position of the particle, what the position(s) of the particle when it’s at rest
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The position function of a particle is given by:

X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t

The velocity function is the derivative of the position:

\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}

The particle will be at rest when the velocity is 0, thus we solve the equation:

2t^2-9t-18=0

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

Substituting:

\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}

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\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

undefined

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