Question

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

Answer 1

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

`a=(\Delta v)/(\Delta t)\iff-5.6\,(\mathrm m)/(\mathrm s^2)=(7.4\,(\mathrm m)/(\mathrm s)-8\,(\mathrm m)/(\mathrm s))/(\Delta t)`

`\implies\Delta t=0.107\,\mathrm s`

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

`\bar v=\frac{7.4\,(\mathrm m)/(\mathrm s)+8\,(\mathrm m)/(\mathrm s)}2=7.7\,(\mathrm m)/(\mathrm s)`

Average velocity is also given by

`\bar v=(\Delta x)/(\Delta t)\iff7.7\,(\mathrm m)/(\mathrm s)=(\Delta x)/(0.107\,\mathrm s)`

so the width of the desk must have been

`\Delta x=0.824\,\mathrm m`

which means C is the most likely answer.