Before the Push Back

Q. A body of mass 0.40 kg moving initially with a constant speed of 10 m/s to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, and the position of the body at that time to be x = 0. What was its position 5 s before the force is applied, at t = –5 s, in metres? expects -50.00 m

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 body of mass 0.40 kg $m = 0.40$ kg moving initially with a constant speed $F_{net} (c) = 0$ N of 10 m/s $v (applied) = 10$ m/s to the north is subject to a constant force of 8.0 N $| F_{p} (p) | = 8.0$ N directed towards the south $F_{p} (p) = - | F_{p} (p) |$ for 30 s. Take the instant the force is applied to be t = 0, and the position of the body at that time to be x = 0 $x (applied) = 0$ m. What was its position 5 s $Δ t_{c} = 5$ s before the force is applied, at t = –5 s, in metres?

The playground

Inputs

mass

m

0.4 kg

speed

v

10.0 m/s

force

| F_{p} |

8 N

earlier

Δ t_{c}

5.00 s

Outputs

position

x

The solution

Solved with NewtonsSecondLaw

Given

$m = 0.40$ kg
$v (applied) = 10$ m/s
$| F_{p} (p) | = 8.0$ N
$Δ t_{c} = 5$ s
$x (applied) = 0$ m from “x = 0”
$F_{net} (c) = 0$ N from “constant speed”
$F_{p} (p) = - | F_{p} (p) |$ from “directed towards the south”

Find $x (earlier_on)$ .

Working

second law(coasting, x) $F_{net} (c) = m \cdot a (c)$
$0 = 0.4 \cdot a (c)$
$a (c) = 0$ m/s²
velocity after a time(coasting, x) $v (applied) = v (earlier_on) + a (c) \cdot Δ t_{c}$
$10 = v (earlier_on) + 0 \cdot 5$
$v (earlier_on) = 10$ m/s
position after a time(coasting, x) $x (applied) = x (earlier_on) + v (earlier_on) \cdot Δ t_{c} + \frac{a (c) \cdot {Δ t_{c}}^{2}}{2}$
$0 = x (earlier_on) + 10 \cdot 5 + \frac{0 \cdot 5^{2}}{2}$
$x (earlier_on) = -50.00 m$

Conclusion

Before the force acts the body just runs on at its steady speed, so the force has no say in where it was.

The Ruby

1require_relative "../physics"23question :before_the_push_back do4  kind :numerical5  describes "A body of mass %{mass} moving initially with a constant speed of %{speed} to the north is subject to a " \6            "constant force of %{force} directed towards the south for 30 s. Take the instant the force is " \7            "applied to be t = 0, and the position of the body at that time to be x = 0. %{position} %{earlier} " \8            "before the force is applied, at t = –5 s, in metres?"9  given mass: "0.40 kg"10  given speed: "10 m/s"11  given force: "8.0 N"12  given earlier: "5 s"13  asks position: "What was its position"14end

1require_relative "../questions/before_the_push_back"2require_relative "../science/laws_of_motion/newtons_second_law"34solve :before_the_push_back, using: NewtonsSecondLaw do5  objects :body, :pusher6  axes :x7  instants :earlier_on, :applied, :later8  body.goes(:coasting, during: earlier_on..applied)9  body.goes(:pushed, during: applied..later)1011  take mass: body.mass12  take speed: body.velocity(at: applied)13  take force: body.force(by: pusher, during: pushed).magnitude14  take earlier: coasting.time_taken1516  deduce_from "directed towards the south", body.force(by: pusher, during: pushed).direction => -x17  deduce_from "x = 0", body.position(at: applied) => "0 m"18  deduce_from "constant speed", body.net_force(during: coasting) => "0 N"1920  position = body.position(at: earlier_on)21  answer position:, in: "m"2223  conclusion "Before the force acts the body just runs on at its steady speed, so the force has no say in " \24             "where it was."25end

1require_relative "../solutions/before_the_push_back"23play_with :before_the_push_back do4  title "Before the Push Back"5end

The laws

quantity	written	units	within	from
volume	$volume$	—	—	Vectors
mass	$m$	kg	0 … ∞	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	$F$	N	—	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
net force	$F_{net}$	N	—	NewtonsSecondLaw
weight	$W$	N	—	NewtonsSecondLaw
displacement of body during coasting along x	$Δ x (c)$	m	—
position of body at applied along x	$x (applied)$	m	—
position of body at earlier on along x	$x (earlier_on)$	m	—
displacement of body during pushed along x	$Δ x (p)$	m	—
position of body at later along x	$x (later)$	m	—
average velocity of body during coasting along x	$v_{av} (c)$	m/s	—
time taken of coasting	$Δ t_{c}$	s	0 … 1e+05
average velocity of body during pushed along x	$v_{av} (p)$	m/s	—
time taken of pushed	$Δ t_{p}$	s	0 … 1e+05
average speed of body during coasting	$c_{av} (c)$	m/s	—
path length of body during coasting	$d (c)$	m	—
average speed of body during pushed	$c_{av} (p)$	m/s	—
path length of body during pushed	$d (p)$	m	—
change of velocity of body during coasting along x	$Δ v (c)$	m/s	—
velocity of body at applied from ground along x	$v (applied)$	m/s	—
velocity of body at earlier on from ground along x	$v (earlier_on)$	m/s	—
change of velocity of body during pushed along x	$Δ v (p)$	m/s	—
velocity of body at later from ground along x	$v (later)$	m/s	—
average acceleration of body during coasting along x	$a_{av} (c)$	m/s²	—
average acceleration of body during pushed along x	$a_{av} (p)$	m/s²	—
acceleration of body during coasting along x	$a (c)$	m/s²	—
acceleration of body during pushed along x	$a (p)$	m/s²	—
net force on body during coasting along x	$F_{net} (c)$	N	—
mass of body	$m$	kg	0 … ∞
net force on body during pushed along x	$F_{net} (p)$	N	—
mass of pusher	$m_{p}$	kg	0 … ∞
weight on ground	$\| W_{g} \|$	N	—
weight on body	$\| W \|$	N	—
weight on pusher	$\| W_{p} \|$	N	—
force on body by pusher during pushed	$\| F_{p} (p) \|$	N	—
force on body by pusher during pushed along x	$F_{p} (p)$	N	—
displacement of body during coasting	$\| Δ x (c) \|$	m	—
position of body at applied	$\| x (applied) \|$	m	—
position of body at earlier on	$\| x (earlier_on) \|$	m	—
displacement of body during pushed	$\| Δ x (p) \|$	m	—
position of body at later	$\| x (later) \|$	m	—
average velocity of body during coasting	$\| v_{av} (c) \|$	m/s	—
average velocity of body during pushed	$\| v_{av} (p) \|$	m/s	—
change of velocity of body during coasting	$\| Δ v (c) \|$	m/s	—
velocity of body at applied from ground	$\| v (applied) \|$	m/s	—
velocity of body at earlier on from ground	$\| v (earlier_on) \|$	m/s	—
change of velocity of body during pushed	$\| Δ v (p) \|$	m/s	—
velocity of body at later from ground	$\| v (later) \|$	m/s	—
average acceleration of body during coasting	$\| a_{av} (c) \|$	m/s²	—
average acceleration of body during pushed	$\| a_{av} (p) \|$	m/s²	—
acceleration of body during coasting	$\| a (c) \|$	m/s²	—
acceleration of body during pushed	$\| a (p) \|$	m/s²	—
net force on body during coasting	$\| F_{net} (c) \|$	N	—
net force on body during pushed	$\| F_{net} (p) \|$	N	—

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

m_{b} \neq 0

has mass?

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 (c) = x (applied) - x (earlier_on)

change of position(coasting, x)

Δ x (p) = x (later) - x (applied)

change of position(pushed, x)

v_{av} (c) = \frac{Δ x (c)}{Δ t_{c}}

displacement a time(coasting, x)

v_{av} (p) = \frac{Δ x (p)}{Δ t_{p}}

displacement a time(pushed, x)

c_{av} (c) = \frac{d (c)}{Δ t_{c}}

path a time(coasting, x)

c_{av} (p) = \frac{d (p)}{Δ t_{p}}

path a time(pushed, x)

Δ v (c) = v (applied) - v (earlier_on)

velocity gained(coasting, x)

Δ v (p) = v (later) - v (applied)

velocity gained(pushed, x)

a_{av} (c) = \frac{Δ v (c)}{Δ t_{c}}

velocity gained a time(coasting, x)

a_{av} (p) = \frac{Δ v (p)}{Δ t_{p}}

velocity gained a time(pushed, x)

v (applied) = v (earlier_on) + a (c) \cdot Δ t_{c}

velocity after a time(coasting, x)

v (later) = v (applied) + a (p) \cdot Δ t_{p}

velocity after a time(pushed, x)

x (applied) = x (earlier_on) + v (earlier_on) \cdot Δ t_{c} + \frac{a (c) \cdot {Δ t_{c}}^{2}}{2}

position after a time(coasting, x)

x (later) = x (applied) + v (applied) \cdot Δ t_{p} + \frac{a (p) \cdot {Δ t_{p}}^{2}}{2}

position after a time(pushed, x)

{v (applied)}^{2} = {v (earlier_on)}^{2} + 2 \cdot a (c) \cdot (x (applied) - x (earlier_on))

velocity after a distance(coasting, x)

{v (later)}^{2} = {v (applied)}^{2} + 2 \cdot a (p) \cdot (x (later) - x (applied))

velocity after a distance(pushed, x)

x (applied) - x (earlier_on) = \frac{(v (applied) + v (earlier_on)) \cdot Δ t_{c}}{2}

mean of the velocities(coasting, x)

x (later) - x (applied) = \frac{(v (later) + v (applied)) \cdot Δ t_{p}}{2}

mean of the velocities(pushed, x)

F_{net} (c) = m \cdot a (c)

second law(coasting, x)

F_{net} (p) = m \cdot a (p)

second law(pushed, x)

F_{net} (p) = F_{p} (p) + 0

net force is the resultant(body, pushed, x)

| Δ x (c) | = \sqrt{{Δ x (c)}^{2}}

magnitude from components(displacement of body during coasting)

| x (applied) | = \sqrt{{x (applied)}^{2}}

magnitude from components(position of body at applied)

| x (earlier_on) | = \sqrt{{x (earlier_on)}^{2}}

magnitude from components(position of body at earlier on)

| Δ x (p) | = \sqrt{{Δ x (p)}^{2}}

magnitude from components(displacement of body during pushed)

| x (later) | = \sqrt{{x (later)}^{2}}

magnitude from components(position of body at later)

| v_{av} (c) | = \sqrt{{v_{av} (c)}^{2}}

magnitude from components(average velocity of body during coasting)

| v_{av} (p) | = \sqrt{{v_{av} (p)}^{2}}

magnitude from components(average velocity of body during pushed)

| Δ v (c) | = \sqrt{{Δ v (c)}^{2}}

magnitude from components(change of velocity of body during coasting)

| v (applied) | = \sqrt{{v (applied)}^{2}}

magnitude from components(velocity of body at applied from ground)

| v (earlier_on) | = \sqrt{{v (earlier_on)}^{2}}

magnitude from components(velocity of body at earlier on from ground)

| Δ v (p) | = \sqrt{{Δ v (p)}^{2}}

magnitude from components(change of velocity of body during pushed)

| v (later) | = \sqrt{{v (later)}^{2}}

magnitude from components(velocity of body at later from ground)

| a_{av} (c) | = \sqrt{{a_{av} (c)}^{2}}

magnitude from components(average acceleration of body during coasting)

| a_{av} (p) | = \sqrt{{a_{av} (p)}^{2}}

magnitude from components(average acceleration of body during pushed)

| a (c) | = \sqrt{{a (c)}^{2}}

magnitude from components(acceleration of body during coasting)

| a (p) | = \sqrt{{a (p)}^{2}}

magnitude from components(acceleration of body during pushed)

| F_{net} (c) | = \sqrt{{F_{net} (c)}^{2}}

magnitude from components(net force on body during coasting)

| F_{net} (p) | = \sqrt{{F_{net} (p)}^{2}}

magnitude from components(net force on body during pushed)

| F_{p} (p) | = \sqrt{{F_{p} (p)}^{2}}

magnitude from components(force on body by pusher during pushed)

F_{p} (p) = - | F_{p} (p) |

directed towards the south

m \neq 0

has mass?(body)

m_{p} \neq 0

has mass?(pusher)

F_{net} (c) = 0

free of forces?(body, coasting)

F_{net} (p) = 0

free of forces?(body, pushed)