<img src="https://tex.z-dn.net/?f=%5Cbold%7BWhat%20%5C%3A%20is%20%5C%3A%20the%20%5C%3A%20speed%3F%20%7D" id="TexFormula1" title=

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2 years ago

"\bold{What \: is \: the \: speed? }" alt="\bold{What \: is \: the \: speed? }" align="absmiddle" class="latex-formula">

Physics

2 answers:

scoray [572]2 years ago

8 0

Refer to the above attachment

STALIN [3.7K]2 years ago

5 0

A mouse runs a distance of 2 meters in 15 seconds.

It's Speed will be 0.13 m/sec.

Average speed =

$\frac{distance}{time}$

Therefore,

Average Speed =

$\frac{2}{15} = 0.1333333 m/sec$

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A 0.40 kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillated with a constant amplitude of 12 cm. Wha

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Answer:

The maximum acceleration of the system is 359.970 centimeters per square second.

Explanation:

The motion of the mass-spring system is represented by the following formula:

$x(t) = A\cdot \cos (\omega \cdot t + \phi)$

Where:

$x(t)$ - Position of the mass with respect to the equilibrium position, measured in centimeters.

$A$ - Amplitude of the mass-spring system, measured in centimeters.

$\omega$ - Angular frequency, measured in radians per second.

$t$ - Time, measured in seconds.

$\phi$ - Phase, measured in radians.

The acceleration experimented by the mass is obtained by deriving the position equation twice:

$a (t) = -\omega^{2}\cdot A \cdot \cos (\omega\cdot t + \phi)$

Where the maximum acceleration of the system is represented by $\omega^{2}\cdot A$ .

The natural frequency of the mass-spring system is:

$\omega = \sqrt{\frac{k}{m} }$

Where:

$k$ - Spring constant, measured in newtons per meter.

$m$ - Mass, measured in kilograms.

If $k = 12\,\frac{N}{m}$ and $m = 0.40\,kg$ , the natural frequency is:

$\omega = \sqrt{\frac{12\,\frac{N}{m} }{0.40\,kg} }$

$\omega \approx 5.477\,\frac{rad}{s}$

Lastly, the maximum acceleration of the system is:

$a_{max} = \left(5.477\,\frac{rad}{s})^{2}\cdot (12\,cm)$

$a_{max} = 359.970\,\frac{cm}{s^{2}}$

The maximum acceleration of the system is 359.970 centimeters per square second.

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