Question 1

A car travels the first half of a 150-mile journey at 45 mi/h and the second half at 75 mi/h. What is the car's average speed for the entire trip?

Accepted Answer

$$\displaystyle 56\ \mathrm{mi/h}$$

Question 2

Convert a speed of $$55.0\ \mathrm{mi/h} to $$meters per second ($$\mathrm{m/s}).$$

Accepted Answer

$$\displaystyle 24.6\ \mathrm{m/s}$$

Question 3

A student walks $$60\ \mathrm{m}$$ from the library to the cafeteria, stopping for $$1$$ minute halfway to talk to a friend. If the walking speed is $$1.5\ \mathrm{m/s}$$, what is the student's average speed for the entire trip?

Accepted Answer

$$\displaystyle 0.6\ \mathrm{m/s}$$

Question 4

If $$8 	imes 10^9$ people stood on the equator, each separated by 2$$\ \mathrm{m}$$, how many times would the line of people circle the Earth, given the equator's length is 4$$ 	imes $$10^7$$\ \mathrm{m}$$?

Accepted Answer

$$\displaystyle 400$$ times

Question 5

The world record for the men's $$100\ \mathrm{m}$$ race is $$9.58\ \mathrm{s}. $$What is the average speed in miles per hour ($$\mathrm{mi/h}$$)? ($$1\ \mathrm{mi} = 1609\ \mathrm{m})$$

Accepted Answer

$$\displaystyle 23.4\ \mathrm{mi/h}$$

Question 6

A pendulum of length $$l = 2\ \mathrm{m}$$ swings through a $$90^\circ$$ arc. Using $$g = 9.8\ \mathrm{m/s^2$}$$, what is the average speed of the sphere at the end of the pendulum during one period?

Accepted Answer

$$\displaystyle 2.2\ \mathrm{m/s}$$

Question 7

Which of the following best defines instantaneous speed?

Accepted Answer

The speed of an object at a specific moment in time.

Question 8

A car travels $$215\ \mathrm{mi}$$ from New York to Boston at a constant speed of $$55\ \mathrm{mi/h}. $$How long does the trip take?

Accepted Answer

$$\displaystyle 3.9\ \mathrm{h}$$

Question 9

Which equation correctly describes the position $$x of an $$object moving at constant velocity $$v$$ along the $$x-$$axis, starting from $$x_0 at$$ $$t=0$$?

Accepted Answer

$$x = x_0$ + vt$$

Question 10

If a person counts $$1$$ bill per second, how many years would it take to count the U.S. national debt of $$37.2$$ trillion dollars in $$100-$$dollar bills?

Accepted Answer

$$\displaystyle 11,800$$ years

Question 11

A graph shows a five-leg journey with segments of constant velocity. If each block is $$100\ \mathrm{m}$$ and the total time is $$26$$ minutes, what is the average speed in $$\mathrm{km/h}$$ for a total distance of $$900\ \mathrm{m}$$?

Accepted Answer

$$\displaystyle 2.08\ \mathrm{km/h}$$

Question 12

Which of the following is the correct formula for the period $$T of a $$simple pendulum of length $$l$$ under gravity $$g$$?

Accepted Answer

$$T = 2\pi \sqrt{l/g}$$

Question 13

Which of the following is a correct definition of average speed?

Accepted Answer

The total distance traveled divided by the total time taken.

Question 14

A car travels $$100\ \mathrm{km} at$$ $$50\ \mathrm{km/h}$$ and then $$100\ \mathrm{km} at$$ $$100\ \mathrm{km/h}. $$What is the average speed for the entire $$200\ \mathrm{km}$$ trip?

Accepted Answer

$$\displaystyle 66.7\ \mathrm{km/h}$$

Question 15

Which of the following is the correct SI unit for speed?

Accepted Answer

$$\displaystyle \mathrm{m/s}$$

Question 16

If $$1\ \mathrm{mi} = 1.609\ \mathrm{km}$$, what is $$88.5\ \mathrm{km/h} in$$ $$\mathrm{mi/h}$$?

Accepted Answer

$$\displaystyle 55.0\ \mathrm{mi/h}$$

Question 17

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total path length traveled; displacement is the straight-line change in position.

Question 18

If $$x = kt^2$, what is the instantaneous velocity v$ at time t$?

Accepted Answer

$$v = 2kt$$

Question 19

Which of the following is the correct definition of the derivative in the context of motion?

Accepted Answer

$$v = \displaystyle \lim_{\Delta t 	o 0} \frac{\Delta x}{\Delta t}$$

Motion at a Constant Speed: Distances, Times, and Powers of Ten

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