twj81403
contestada

A student slides a book across a desk, with a velocity of +8 m/s. When her friend catches the book, it has a velocity of +7.4 m/s. If the acceleration was a constant -5.6 m/s2, how wide is the desk?

A. 0.05 m
B. 0.60 m
C. 0.83 m
D. 1.65 m

Respuesta :

Because acceleration was constant throughout the slide, we can show the slide lasted

[tex]a=\dfrac{\Delta v}{\Delta t}\iff-5.6\,\dfrac{\mathrm m}{\mathrm s^2}=\dfrac{7.4\,\frac{\mathrm m}{\mathrm s}-8\,\frac{\mathrm m}{\mathrm s}}{\Delta t}[/tex]

[tex]\implies\Delta t=0.107\,\mathrm s[/tex]

Also because accleration was constant, we know the average velocity of the book was

[tex]\bar v=\dfrac{7.4\,\frac{\mathrm m}{\mathrm s}+8\,\frac{\mathrm m}{\mathrm s}}2=7.7\,\dfrac{\mathrm m}{\mathrm s}[/tex]

Average velocity is also given by

[tex]\bar v=\dfrac{\Delta x}{\Delta t}\iff7.7\,\dfrac{\mathrm m}{\mathrm s}=\dfrac{\Delta x}{0.107\,\mathrm s}[/tex]

so the width of the desk must have been

[tex]\Delta x=0.824\,\mathrm m[/tex]

which means C is the most likely answer.

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