Q: A runner accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for $$5$$ seconds. What is her final velocity?

$$v = a t = 2 \times 5 = 10\ \mathrm{m/s}$$

Q: A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$Neglecting air resistance, what is its velocity after $$2$$ seconds? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward)

$$v = 15 - 9.8 \times 2 = -4.6\ \mathrm{m/s} ($$downward)

Q: A cyclist travels at a constant velocity of $$12\ \mathrm{m/s}$$ for $$30$$ seconds. What is the total displacement?

$$12 \times 30 = 360\ \mathrm{m}$$

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

A car moves 60 meters east, then 80 meters north. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{60^2$ + 80^2$} = 100$$ meters

Question 3

Which equation correctly represents average velocity $$\vec{v}_{avg}$$ over a time interval $$\Delta t$$?

Accepted Answer

$$\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$$

Question 4

A runner accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for $$5$$ seconds. What is her final velocity?

Accepted Answer

$$v = a t = 2 	imes 5 = 10\ \mathrm{m/s}$$

Question 5

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 6

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$Neglecting air resistance, what is its velocity after $$2$$ seconds? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward)

Accepted Answer

$$v = 15 - 9.8 	imes 2 = -4.6\ \mathrm{m/s} ($$downward)

Question 7

Which prefix represents $$10^{-6} in SI $$units?

Accepted Answer

micro

Question 8

A cyclist travels at a constant velocity of $$12\ \mathrm{m/s}$$ for $$30$$ seconds. What is the total displacement?

Accepted Answer

$$12 	imes 30 = 360\ \mathrm{m}$$

Question 9

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity.

Question 10

A car slows down from $$20\ \mathrm{m/s} to$$ $$5\ \mathrm{m/s} in$$ $$3$$ seconds. What is its average acceleration?

Accepted Answer

$$a = \frac{5 - 20}{3} = -5\ \mathrm{m/s^2$}$$

Question 11

Which equation gives the displacement $$\Delta x$$ for constant acceleration?

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$

Question 12

A student walks $$4$$ meters east, $$3$$ meters north, and $$2$$ meters west. What is the magnitude of her total displacement?

Accepted Answer

$$\sqrt{(4-2)^2$ + 3^2$} = \sqrt{4 + 9} = \sqrt{13} \approx 3.6$$ meters

Question 13

Which of the following is NOT a base SI unit?

Accepted Answer

liter

Question 14

A car travels at $$15\ \mathrm{m/s}$$ for $$10$$ seconds, then at $$25\ \mathrm{m/s}$$ for $$5$$ seconds. What is the average speed for the whole trip?

Accepted Answer

$$\frac{15 	imes 10 + 25 	imes 5}{10 + 5} = \frac{150 + 125}{15} = \frac{275}{15} \approx 18.33\ \mathrm{m/s}$$

Question 15

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity at a specific moment in time.

Question 16

A train moves with a constant acceleration of $$2\ \mathrm{m/s^2$}$$ from rest. How far does it travel in $$8$$ seconds?

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} 	imes 2 	imes 8^2$ = 64$$ meters

Question 17

Which of the following is the correct formula for average acceleration $$a_{avg}$$?

Accepted Answer

$$a_{avg} = \frac{\Delta v}{\Delta t}$$

Question 18

A car moves in a straight line with a velocity given by $$v = 5 + 2t$$ ($$v in m/s$$, $$t in s). $$What is its acceleration?

Accepted Answer

$$a = \frac{dv}{dt} = 2\ \mathrm{m/s^2$}$$

Kinematics: Motion, Vectors, and Units – Study Notes

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