The Long Way Round: Speed

Q. A hotel is 10 km from the station along a straight road, but a dishonest driver takes a 23 km route and gets there in 28 min. What is the taxi's average speed, in km/h? expects 49.3 km/h

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A hotel is 10 km from the station along a straight road, but a dishonest driver takes a 23 km $d = 23$ km route and gets there in 28 min $Δ t = 28$ min. What is the taxi's average speed, in km/h?

The playground

Inputs

route

d

23 km

time

Δ t

28 min

Outputs

average speed

c_{av}

The solution

Solved with MotionInAPlane

Given

$d = 23$ km
$Δ t = 28$ min

Find $c_{av}$ .

Working

$d = 23$ km $= 23000$ m
$Δ t = 28$ min $= 1680$ s
path a time $c_{av} = \frac{d}{Δ t}$
$c_{av} = \frac{23000}{1680}$
$c_{av} = 49.29$ km/h
$c_{av} = 13.6904762$ m/s $= 49.2857143$ km/h
$c_{av} \approx 49.3$ km/hto 3 significant figures

Conclusion

Average speed counts the whole of the road driven, however roundabout.

The Ruby

1require_relative "../physics"23question :the_long_way_round_speed do4  kind :numerical5  describes "A hotel is 10 km from the station along a straight road, but a dishonest driver takes a " \6          "%{route} route and gets there in %{time}. %{average_speed}, in km/h?"7  given route: "23 km"8  given time: "28 min"9  asks average_speed: "What is the taxi's average speed"10end

1require_relative "../questions/the_long_way_round_speed"2require_relative "../science/motion_in_a_plane/motion_in_a_plane"34solve :the_long_way_round_speed, using: MotionInAPlane do5  take route: :d, time: :Delta_t6  take average_speed: :c_av7  answer find_value(:average_speed, in: "km/h", figures: 3)89  conclusion "Average speed counts the whole of the road driven, however roundabout."10end

1require_relative "../solutions/the_long_way_round_speed"23play_with :the_long_way_round_speed do4  title "The Long Way Round: Speed"5end

The laws

quantity	written	units	within	from
volume	$volume$	—	—	Vectors
mass	$mass$	—	—	Vectors
speed	$speed$	—	—	Vectors
density	$density$	—	—	Vectors
number of moles	$n$	—	—	Vectors
angular frequency	${angular}_{frequency}$	—	—	Vectors
work	$work$	—	—	Vectors
current	$current$	—	—	Vectors
temperature	$temperature$	—	—	Vectors
pressure	$pressure$	—	—	Vectors
time	$t$	s	0 … 1e+05	Vectors
power	$power$	—	—	Vectors
total path length	$s$	—	—	Vectors
energy	$energy$	—	—	Vectors
gravitational potential	${gravitational}_{potential}$	—	—	Vectors
coefficient of friction	$μ$	—	—	Vectors
charge	$charge$	—	—	Vectors
acceleration	$a$	m/s²	—	Vectors
velocity	$v$	m/s	—	Vectors
displacement	$Δ x$	m	—	Vectors
angular velocity	${angular}_{velocity}$	—	—	Vectors
force	$force$	—	—	Vectors
angular momentum	${angular}_{momentum}$	—	—	Vectors
linear momentum	$p_{lin}$	—	—	Vectors
electric field	${electric}_{field}$	—	—	Vectors
average velocity	$v_{av}$	m/s	—	Vectors
magnetic moment	${magnetic}_{moment}$	—	—	Vectors
relative velocity	$v_{AB}$	—	—	Vectors
impulse	$impulse$	—	—	Vectors
first vector	$A$	—	0 … ∞	Vectors
second vector	$B$	—	0 … ∞	Vectors
angle between	$φ$	—	0 … 3.142	Vectors
resultant	$R$	—	0 … ∞	Vectors
resultant direction	$β$	—	0 … 3.142	Vectors
direction	$α$	—	-3.142 … 3.142	Vectors
x component	$A_{x}$	—	—	Vectors
y component	$A_{y}$	—	—	Vectors
position	$x$	m	—	Velocity
path length	$d$	m	—	Velocity
time taken	$Δ t$	s	0 … 1e+05	Velocity
average speed	$c_{av}$	m/s	—	Velocity
starting position	$x_{0}$	m	—	Velocity
final position	$x$	m	—	Velocity
change of velocity	$Δ v$	m/s	—	Acceleration
average acceleration	$a_{av}$	m/s²	—	Acceleration
starting velocity	$v_{0}$	m/s	—	Acceleration
final velocity	$v$	m/s	—	Acceleration
gravity	$g$	m/s²	—	UniformAcceleration

x_{0} \equiv x_{i} (start of motion)

starting position

x \equiv x_{i} (end of motion)

final position

v_{0} \equiv v_{i} (start of motion)

starting velocity

v \equiv v_{i} (end of motion)

final velocity

t \equiv Δ t_{m}

time

A = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}}

magnitude from components

d_{i} (whole) = d_{i} (part 1) + d_{i} (part 2)

path in parts

Δ t_{w} = Δ t_{p} + Δ t_{p}

time in parts

a_{i} (part 1) = a_{i} (whole)

steady through its parts

v_{o,x} (t) = v_{o} (t) \cdot \cos θ_{o} (t)

parts of a velocity

R^{2} = A^{2} + B^{2} + 2 \cdot A \cdot B \cdot \cos φ

law of cosines

R \cdot \sin β = B \cdot \sin φ

law of sines

R \cdot \cos β = A + B \cdot \cos φ

along the first

A_{x} = A \cdot \cos α

resolved along x

A_{y} = A \cdot \sin α

resolved along y

Δ x = x - x_{0}

change of position

v_{av} = \frac{Δ x}{Δ t}

displacement a time

c_{av} = \frac{d}{Δ t}

path a time

Δ v = v - v_{0}

velocity gained

a_{av} = \frac{Δ v}{Δ t}

velocity gained a time

v = v_{0} + a \cdot t

velocity after a time

x = x_{0} + v_{0} \cdot t + \frac{a \cdot t^{2}}{2}

position after a time

v^{2} = {v_{0}}^{2} + 2 \cdot a \cdot (x - x_{0})

velocity after a distance

x - x_{0} = \frac{(v + v_{0}) \cdot t}{2}

mean of the velocities