Scalars and Vectors in One Dimension Practice

Sample questions

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1. Sample 1difficulty 2/5

   A runner jogs $400~\text{m}$ east, then $300~\text{m}$ west, all in $350~\text{s}$. What is the magnitude of her <strong>average velocity</strong>?

   • A

     $1.0~\text{m/s}$

   • B

     $0.57~\text{m/s}$

   • C

     $2.0~\text{m/s}$

   • D

     $0.29~\text{m/s}$

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   Why

   Net displacement is $400 - 300 = 100~\text{m}$ east, so $\bar v = 100/350 \approx 0.29~\text{m/s}$. (Average <strong>speed</strong> would use total distance $700~\text{m}$.)

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2. Sample 2difficulty 2/5

   A particle moves from position $\vec r_1 = (3, 4)~\text{m}$ to $\vec r_2 = (-1, 7)~\text{m}$. What is the magnitude of its displacement?

   • A

     $11~\text{m}$

   • B

     $7~\text{m}$

   • C

     $3~\text{m}$

   • D

     $5~\text{m}$

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   Why

   $\Delta\vec r = (-4, 3)$. $|\Delta\vec r| = \sqrt{16 + 9} = 5~\text{m}$.

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3. Sample 3difficulty 2/5

   A boat heads due north at $4~\text{m/s}$ across a river that flows east at $3~\text{m/s}$. What is the boat's speed relative to the riverbank?

   • A

     $7~\text{m/s}$

   • B

     $1~\text{m/s}$

   • C

     $5~\text{m/s}$

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   • D

     $12~\text{m/s}$

   Why

   $v = \sqrt{4^2 + 3^2} = \sqrt{25} = 5~\text{m/s}$.

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