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Mathematics

1 answer:

S_A_V [24]1 year ago

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Answer:

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Step-by-step explanation:

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2 years ago

Solve the seperable equation: dx/dt=3xt^2

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$\displaystyle
\dfrac{dx}{dt}=3xt^2\\
\dfrac{dx}{x}=3t^2 \, dt\\
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2 years ago

A police cruiser is traveling at 20.0 m/s when the officer spies a speeder. The cruiser accelerates at 3.0 m/s^2 for 5.0 seconds

Tema [17]

For the first 5.0 seconds, the cruiser covers a distance of

$\left(20.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2=137.5\,\mathrm m$

At this point, the cruiser will have achieved a velocity of

$\left(20.0\dfrac{\rm m}{\rm s}\right)+\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)=35\dfrac{\rm m}{\rm s}$

The cruiser will take

$\left(35\dfrac{\rm m}{\rm s}\right)-\left(5.0\dfrac{\rm m}{\mathrm s^2}\right)t=0\implies t=7.0\,\mathrm s$

to come to a stop as it decelerates. It will have covered a total distance of

$(137.5\,\mathrm m)+\left(35\dfrac{\rm m}{\rm s}\right)(7.0\,\mathrm s)+\dfrac12\left(-5.0\dfrac{\rm m}{\mathrm s^2}\right)(7.0\,\mathrm s)^2=\boxed{260\,\mathrm m}$