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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