Q: A boat moves east at $$5\ \text{m/s}$$ relative to the water, while the water flows north at $$3\ \text{m/s}$$ relative to the shore. What is the boat's speed relative to the shore?

$$\sqrt{5^2$ + 3^2$} = 5.83\ \text{m/s}$$

Question 1

A car travels 120 meters in 10 seconds. What is its average velocity?

Accepted Answer

$$12\ 	ext{m/s}$$

Question 2

A ball is thrown straight upward with an initial velocity of $$15\ 	ext{m/s}. $$Ignoring air resistance, what is the maximum height it reaches? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$11.5\ 	ext{m}$$

Question 3

Which equation best describes the position $$x(t) of an $$object moving with constant velocity $$v$$ from an initial position $$x_0$$?

Accepted Answer

$$x(t) = x_0$ + v t$$

Question 4

A projectile is launched at $$30\ ^\circ$$ above the horizontal with a speed of $$20\ 	ext{m/s}. $$What is the initial vertical component of its velocity?

Accepted Answer

$$10\ 	ext{m/s}$$

Question 5

If a train accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$5\ 	ext{s}$$, what is its final velocity?

Accepted Answer

$$10\ 	ext{m/s}$$

Question 6

A runner moves from $$x = 0 to$$ $$x = 50\ 	ext{m} in$$ $$8\ 	ext{s}$$, then returns to $$x = 20\ 	ext{m} in$$ $$4\ 	ext{s}. $$What is the average velocity for the entire trip?

Accepted Answer

$$1.67\ 	ext{m/s}$$

Question 7

A stone is dropped from a bridge and hits the water $$2\ 	ext{s}$$ later. What is the height of the bridge above the water? (Ignore air resistance, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$19.6\ 	ext{m}$$

Question 8

Which formula gives the final velocity $$v_f of an $$object after traveling a displacement $$\Delta y$$ with constant acceleration $$a$$ from initial velocity $$v_i$$?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2 a \Delta y$$

Question 9

A boat moves east at $$5\ 	ext{m/s}$$ relative to the water, while the water flows north at $$3\ 	ext{m/s}$$ relative to the shore. What is the boat's speed relative to the shore?

Accepted Answer

$$\sqrt{5^2$ + 3^2$} = 5.83\ 	ext{m/s}$$

Question 10

A car accelerates from $$10\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is its average acceleration?

Accepted Answer

$$5\ 	ext{m/s}^2$$

Question 11

A projectile is launched horizontally from a $$45\ 	ext{m}$$ high cliff. How long does it take to hit the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$3.03\ 	ext{s}$$

Question 12

A vector has components $$x = -4$$ and $$y = 3. $$What is its magnitude?

Accepted Answer

$$5$$

Question 13

A car travels $$60\ 	ext{km} in$$ $$1.5\ 	ext{hours}. $$What is its speed in $$	ext{m/s}$$?

Accepted Answer

$$11.1\ 	ext{m/s}$$

Question 14

A ball is thrown at $$25\ 	ext{m/s} at an $$angle of $$60^\circ$$ above the horizontal. What is the horizontal component of its velocity?

Accepted Answer

$$12.5\ 	ext{m/s}$$

Question 15

A car moves at $$20\ 	ext{m/s}$$ for $$5\ 	ext{s}$$, then at $$30\ 	ext{m/s}$$ for $$5\ 	ext{s}. $$What is its average velocity over the $$10\ 	ext{s}$$?

Accepted Answer

$$25\ 	ext{m/s}$$

Question 16

A ball is thrown downward from a $$20\ 	ext{m}$$ tall building with an initial velocity of $$5\ 	ext{m/s}. $$How long does it take to reach the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$1.53\ 	ext{s}$$

Question 17

A vector points $$30^\circ$$ above the positive $$x-$$axis and has a magnitude of $$10. $$What are its $$x$$ and $$y$$ components?

Accepted Answer

$$x = 8.66,\ y = 5$$

Question 18

A car travels $$100\ 	ext{m} in$$ $$5\ 	ext{s}$$, then $$50\ 	ext{m} in$$ $$2\ 	ext{s}. $$What is its average velocity for the entire trip?

Accepted Answer

$$21.43\ 	ext{m/s}$$

Question 19

A ball is thrown horizontally from a $$10\ 	ext{m}$$ high table. How long does it take to hit the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$1.43\ 	ext{s}$$

Question 20

A car moves at $$15\ 	ext{m/s}$$ for $$3\ 	ext{s}$$, then at $$25\ 	ext{m/s}$$ for $$2\ 	ext{s}. $$What is the total displacement?

Accepted Answer

$$85\ 	ext{m}$$

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