Explanation:
a.)
We find the relative speed
u = vb + vc
b.)
chuck and the cart are at a rest position
mcartvc = mballvb
from part a above,
vc = u - vb
mcartu = vb(mcart + mball)
make vb the subject of the equation
[tex]vb=\frac{mcartu}{mcart +mball}[/tex]
c.)
from anser a,
vb = u - vc
then mcart vc = mball(u-vc)
[tex]vc= \frac{Mballu}{Mcart+Mball}[/tex]
d.
Mballvb = (Mcart + Mball)vj
we make vj the subject to get her relative speed
[tex]vj=\frac{MballVb}{Mcart+Mball}[/tex]
e.
given the solution in part d above,
we have
[tex]vj=\frac{MballVb}{Mcart+Mball}[/tex]
remember,
vb = u - vc
such that
[tex]Vj = \frac{Mball(u-v)}{Mball +Mcart}[/tex]
thank you!
the boiling point of F2 much lower than the boiling point of NH3
Answer:yeah it A
Explanation:
5. Charges added to a conductor quickly spread over the surface of the object.
a. True
b. False
Answer:
a. True
Explanation:
Conduction involves the transfer of electric charge or thermal energy due to the movement of particles. When the conduction relates to electric charge, it is known as electrical conduction while when it relates to thermal energy, it is known as heat conduction.
A conductor can be defined as any material or physical object that allows the conduction (transfer) of electric charge or thermal energy. Some examples of conductors are metal, steel, aluminum, copper, frying pan, pot, metallic spoon, etc.
During heat conduction, thermal energy is usually transferred from fast moving particles to slow moving particles during the collision of these particles.
Furthermore, any charge that is added to a conductor would quickly spread over the surface of the conducting object due to the fact that it allows the movement of subatomic particles.
Answer: True
Explanation: Aced Test
Identical net forces act for the same length of time on two different spherical masses. Which of the following describes the change in linear momentum of the smaller mass compared to that of the larger mass?
a. it is smaller than the change in linear momentum of the larger mass but not zero.
b. It is larger than the change in linear momentum of the larger mass.
c. It is equal to the change in linear momentum of the larger mass.
d. It is zero
Answer:
the correct answer is c
Explanation:
In this exercise we seek the momentum
I = F t
this value is set because forces and time are given.
Now we can use the relationship between linear momentum and momentum
I = p_f - p₀
I = m v_f - m v₀
suppose that the two spheres depart with the same initial velocity
Let's analyze these results, the value of the impulse is the same, so the body of lower mass must acquire greater speed or momentum
consequently the lighter sphere acquires more final speed, but the change of momentum is the same in the two spheres
Consequently the correct answer is c
A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell.
Required:
a. What is the charge on the inner surface of the shell?
b. What is the charge on the outer surface of the shell?
Answer:
(a) Negative Q
(b) Positive Q
Explanation:
Charge is the inherent property of matter due to the transference of electrons.
There are three methods of charging a body.
(i) Charging by friction: When two uncharged bodies rubbed together, then one body gets positive charged and the other is negatively charges it is due to the transference of electrons form one body to another.
(ii) Conduction: when a charged body comes in contact with the another uncharged body, the uncharged body gets the same charge and the charge is distributed equally.
(iii) Induction: When a uncharged body keep near the charged body, the uncharged body gets the same amount of charge but opposite in sign.
(a) When a small tack of charge Q is lowered into the hole, then due to the process of induction, the charge on the inner surface of the shell is - Q.
(b) Due to the process of conduction, the charge on the outer surface of the shell is Q.
The charge on the inner surface of the shell is negative whereas the charge on the outer surface of the shell is positive.
Reasons for change of charge on a body
Due to the process of induction the inner surface of the shell creates negative charge because when a uncharged body bring near to the charged body, the uncharged body gets the same amount of charge but opposite in sign.
While on the other hand, there is no charge interaction with the outer surface so it remains positively charge so we can conclude that the charge on the inner surface of the shell is negative whereas the charge on the outer surface of the shell is positive.
Learn more about charge here: https://brainly.com/question/18102056
what is potential energy??
Answer:
the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.
hope this helps
have a good day :)
Explanation:
Answer:
Potential Energy is the stored energy in an object or system because of its position or configuration.
Explanation:
Example: Water at the top of a waterfall, before the precipice.
A 20-g bullet is shot vertically into an 2.8-kg block. The block lifts upward 9 mm. The bullet penetrates the block and comes to rest in it in a time interval of 5 ms. Assume the force on the bullet is constant during penetration and that air resistance is negligible. What is the speed of the bullet just before the impact
Answer:
The speed of the bullet just before the impact is 701 m/s
Explanation:
Given;
mass of the bullet, m₁ = 20 g = 0.02 kg
mass of the block, m₂ = 2.8 kg
displacement of the block, d = 9 mm = 9 x 10⁻³ m
duration of motion of the bullet, t = 5 ms = 5 x 10⁻³ s
Apply the principle of conservation of energy;
The final kinetic energy of the bullet = maximum potential energy of the block
[tex]\frac{1}{2} m_1v^2 = m_2gh\\\\v^2 = \frac{2m_2gh}{m_1} \\\\v= \sqrt{\frac{2m_2gh}{m_1} } \\\\v = \sqrt{\frac{2 \times 2.8 \times 9.8 \times (9\times 10^{-3})}{0.02} } \\\\v = 4.97 \ m/s[/tex]
Apply the principle of conservation of linear momentum, to determine the initial velocity of the bullet before the impact.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
u₁ is the initial velocity of the bullet
u₂ is the initial velocity of the block = 0
m₁u₁ + 0 = v(m₁ + m₂)
m₁u₁ = v(m₁ + m₂)
0.02u₁ = 4.97(2.8 + 0.02)
0.02u₁ = 14.02
u₁ = 14.02 / 0.02
u₁ = 701 m/s
Therefore, the speed of the bullet just before the impact is 701 m/s
Name the state of matter in which
(a) Rate of diffusion is fastest (b) diffusion does not take place.
plss essay
Answer:
A
Explanation:
g If we decreased the wavelength by a factor of 2 and also increased the distance D by a factor of 2, the fringes on the screen would be...
Answer:
y = y₀ / 4
Explanation:
In a double slit experiment the constructive interference lines are given by
d sin θ = m λ
if we use trigonometry
tan θ = y / L
as in these experiments the angles are very small
tan θ = sin θ /cos θ = sin θ
we substitute
sin θ = y / L
d y / L = m λ
let's use a subscript "o" for the initial values
I = m λ₀ L /d₀
They ask us to decrease the wavelength by 2
λ = λ₀ / 2
the distance in the slit is increased by a factor of two
d = 2 d₀
we substitute
2d₀ y/L = m λ₀/2
y = m λ₀ L/d₀ ¼
y = y₀ / 4
PLS ANSWER WORTH 10 POINTS PLS HELP
Answer:
the answer should be D
Explanation:
Because if you want to earn your goals you must complete small goals to earn big goals
A parallel plate vacuum capacitor has 8.40 J of energy stored. The separation between plates is 2.30 mm. If the separation is decreased to 1.15 mm what is the energy stored if (a) the charge Q on the plates is held constant, and (b) the voltage V across the plates is held constant
(a) 4.20 J
(b) 16.74 J
Explanation:For a parallel plate vacuum capacitor with area A and whose plates are separated by by a distance of d, its capacitance C is given by;
C = A∈₀ / d --------------------(i)
Where;
∈₀ = constant called permittivity of vacuum.
The energy U stored in such capacitor is given by;
U = [tex]\frac{1}{2}[/tex]CV² ----------------------(ii)
or
U = [tex]\frac{1}{2}[/tex](Q²/C) -------------------(**)
Where;
V = potential difference or voltage across the plates.
Q = charge on the plates.
(a) If the charge is held constant
Combine equations (i) and (**) to give;
U = [tex]\frac{1}{2}[/tex]Q² / (A∈₀ / d) -----------------------(iii)
From the question;
The parallel plate capacitor has 8.40J energy stored and distance between plates is 2.30mm i.e
U = 8.40J
d = 2.30mm = 0.023m
Substitute these values into equation (iii)
8.40 = [tex]\frac{1}{2}[/tex]Q² / (A∈₀ / 0.023)
8.40 = [tex]\frac{1}{2}[/tex]Q² x (0.023 / A∈₀)
Multiply through by 2
2 x 8.40 = Q² x (0.023 / A∈₀)
16.80 = Q² x (0.023 / A∈₀)
Divide through by 0.023
16.80 / 0.023 = Q² x (0.023 / A∈₀) / 0.023
730.4 = Q² / (A∈₀)
Make Q² subject of the formula
Q² = 730.4(A∈₀)
Now, if the separation distance is decreased to 1.15mm and the voltage is held constant i.e
d = 1.15mm = 0.0115m
Q = constant [this means that Q² still remains 730.4(A∈₀) ]
The energy stored is found by substituting these values of d and Q² into equation (iii) as follows;
U = [tex]\frac{1}{2}[/tex]Q² / (A∈₀ / d)
U = [tex]\frac{1}{2}[/tex](730.4(A∈₀)) / (A∈₀ / 0.0115)
U = [tex]\frac{1}{2}[/tex](730.4(A∈₀))(0.0115 / A∈₀)
U = [tex]\frac{1}{2}[/tex](730.4)(0.0115)
U = 4.20J
Therefore, the energy stored if the charge Q on the plates is held constant is 4.20 J
(b) If the voltage is held constant
Combine equations (i) and (ii) to give;
U = [tex]\frac{1}{2}[/tex](A∈₀ / d)V² -----------------------(iv)
From the question;
The parallel plate capacitor has 8.40J energy stored and distance between plates is 2.30mm i.e
U = 8.40J
d = 2.30mm = 0.023m
Substitute these values into equation (iv)
8.40 = [tex]\frac{1}{2}[/tex](A∈₀ / 0.023)V²
Multiply through by 2 x 0.023
2 x 0.023 x 8.40 = (A∈₀)V²
2 x 0.023 x 8.40 = (A∈₀)V²
0.385 = (A∈₀)V²
Make V² subject of the formula
V² = 0.385/(A∈₀)
Now, if the separation distance is decreased to 1.15mm and the voltage is held constant i.e
d = 1.15mm = 0.0115m
V = constant [this means that V² still remains 0.385/(A∈₀) ]
The energy stored is found by substituting these values of d and V² into equation (iv) as follows;
U = [tex]\frac{1}{2}[/tex](A∈₀ / 0.0115)[0.385/(A∈₀)]
U = [tex]\frac{1}{2}[/tex](0.385/0.0115)
U = 16.74
Therefore, the energy stored if the voltage V across the plates is held constant is 16.74 J
The Heat Force
이
18
1 point
-
If two objects are the same temperature and are physically touching which of the following would be true?
The objects would be in thermodynamic equilibrium and would transfer energy through conduction.
ОООО
1
The objects would not be in thermodynamic equilibrium and heat would transfer through conduction.
The objects would not be in thermodynamic equilibrium and as a result there would be no heat transfer
The objects would be in thermodynamic equilibrium and as a result there would be no heat transfer.
2
If two objects are the SAME temperature and are physically touching,
then
. . .
. . .
. . .
The objects would be in thermodynamic equilibrium and as a result there would be no heat transfer.
Jesse drives 120km to a farm. His trip takes 2 1/2 hoursWhat is his speed?
Speed = distance / time
Speed = 120 km / 2 1/2 hours
Speed = 48 km per hour
Who is a socio-economically disadvantaged child? Explain any four ways forhelping such a child
Explanation:
A socio-economically disadvantaged child is the one who is disadvantaged in terms of social position and economic position. Such children have limited resources in terms of education, money and future options. Four ways of helping such children are as follows:
1) Help them in education - You can help such children by giving them free tuition. If you belong to a well off family, you can get them admitted in schools as well. Provide them with books and uniform.
2) Encourage them to do well in school and pursue their passions.
3) Provide them with meals, if they do not have access to regular meals.
4) encourage them to go school regularly.
Answer:
sorry i dont know the answer bit mark me as BRAINLISTTerminal velocity. A rider on a bike with the combined mass of 100kg attains a terminal speed of 15m/s on a 12% slope. Assuming that the only forces affecting the speed are the weight and the drag, calculate the drag coefficient. The frontal area is 0.9m2 .
Answer:
0.9378
Explanation:
Weight (W) of the rider = 100 kg;
since 1 kg = 9.8067 N
100 kg will be = 980.67 N
W = 980.67 N
At the slope of 12%, the angle θ is calculated as:
[tex]tan \ \theta = \dfrac{12}{100} \\ \\ tan \ \theta = 0.12 \\ \\ \theta = tan^{-1}(0.12) \\\\ \theta = 6.84^0[/tex]
The drag force D = Wsinθ
[tex]\dfrac{1}{2}C_v \rho AV^2 = W sin \theta[/tex]
where;
[tex]\rho = 1.23 \ kg/m^3[/tex]
A = 0.9 m²
V = 15 m/s
∴
Drag coefficient [tex]C_D = \dfrac{2 *W*sin \theta}{\rho *A *V^2}[/tex]
[tex]C_D =\dfrac{2 *980.67*sin 6.84}{1.23 *0.9 *15^2}[/tex]
[tex]C_D =0.9378[/tex]
A disk-shaped platform has a known rotational inertia ID. The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of ÏD in the counterclockwise direction as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant.
In a different experiment, the original disk is replaced with a disk for which frictional forces are considered to be negligible. The disk is set into motion such that it rotates with a constant angular speed. As the disk spins, a small sphere of clay is dropped onto the disk, and the sphere sticks to the disk.
Required:
Write down the claims which are correct about the angular momentum and the total kinetic energy of the disk-sphere system immediately before and immediately after the collision.
Answer:
Explanation:
The angular momentum of that same disk-sphere remains unchanged the very same way before and after the impact of the collision when the clay sphere adheres to the disk.
[tex]\mathbf{I_w}[/tex] = constant.
The overall value of such moment of inertia is now altered when the clay spherical sticks. Due to the inclusion of the clay sphere, the moment of inertia will essentially rise. As a result of this increase, the angular speed w decreases in value.
Recall that:
The Kinetic energy is given by:
[tex]\mathbf{K = \dfrac{1}{2} Iw^2} \\ \\\mathbf{K = \dfrac{1}{2} lw*w}[/tex]
where;
[tex]\mathbf{I_w}[/tex] is constant and w reduces;
As a result, just after the collision, the system's total kinetic energy decreases.
The total kinetic energy of the system decreases after the collision.
What is angular momentum?The angular momentum of any rotating body is defined as the product of the moment of inertia of the body and the angular velocity of the body.
Now from the question, we can see that the angular momentum of the body remains constant before and after the impact of the collision when the clay sphere adheres to the disk.
So angular momentum will be
[tex]Iw[/tex] = constant.
The overall value of such a moment of inertia is now changed when the clay spherical sticks. Due to the inclusion of the clay sphere, the moment of inertia will essentially rise. As a result of this increase, the angular speed w decreases in value.
The Kinetic energy is given by:
[tex]KE=\dfrac{1}{2} Iw^2[/tex]
[tex]KE= \dfrac{1}{2} Iw\times w[/tex]
Since the angular momentum [tex]Iw[/tex] is constant and w is reducing then ultimately the energy of the system is decreasing.
Thus the total kinetic energy of the system decreases after the collision.
To know more about Angular momentum follow
https://brainly.com/question/25677703
Two physics students are arguing about superconductors and their discovery, Jeffe says that he can use a
thermometer and a plug that generates electric current to mimic the experiment and make a superconductor since the
thermometer contains mercury. Sigorne says that he is wrong. Who should win the argument?
O Sigorne, because Jeffe can't use mercury to create a superconductor
O Sigorne, because Jeffe would have to cool the mercury as well
O Jeffe, because he has all of the materials to make a superconductor
O Jeffe, because superconductors are simple to make as long as there is a metal and a current
Answer:
B on edge2020-2021
Explanation:
You drop a ball from a height of 10 meters. Each time the ball bounces, it
reaches a lower height. Why does the ball lose height after each time it hits
the ground?
A 50 kg child sits on the left side of the bathtub. A small toy boat of 0.5 kg is on the right side of the bathtub. Which part of the bathtub has the greatest pressure
Answer:
Option 2
Explanation:
The complete question is
A 50 kg child sits on the left side of the bathtub. A small toy boat of 0.5 kg is on the right side of the bathtub. Which part of the bathtub has the greatest pressure
TopBottomLeftRightSolution
It is the bottom of the bucket that will high pressure because of the additional weight of 50 Kg boy along with the weight of the water and the tub itself.
Pressure acts in the down ward direction and is equal to the force/weight divided by the area.
Hence, option 2 is correct
Each of the four expansion models (recollapsing, critical, coasting, and accelerating) predict different ages for the universe, given the current expansion rate. Why is this
Answer:
This is because the age of the universe is determined by the pace of expansion in the past, and each model forecasts a different pace.
Explanation:
The age of the universe is determined by the pace of expansion in the past, and each model forecasts a different pace.
This is due to the fact that the expansion rate in the coasting model is constant and never changes. Because the cosmos is growing faster now than during the old days, recollapsing and critical models give shorter ages. According to the accelerating model, the universe is growing at a slower rate currently than in the past, implying an older age.
what's the difference between mass and inertia in a tabular form
Answer:
to be honest i dont know
Explanation:
^^
Before the 1970's, energy prices were A. relatively low B. extremely burdensome C. incredibly high D. very problematic
Answer:
C
Explanation:
correct me if I'm wrong.
Answer:
A
Explanation:
i got it right on acellus
A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 20 centimeters to 50 centimeters
Answer:
52.5 J
Explanation:
Applying,
Hook's law,
F = ke............... Equation 1
Where F = Force, k = spring constant, e = extension.
make k the subject of the equation
k = F/e............ Equation 2
From the question,
Given: F = 350 Newtons, e = 30 cm = 0.3 m
Substitute these values into equation 2
k = 350/0.3 N/m
Also,
W = 1/2(ke²).................. Equation 3
Where W = work done in stretching the spring.
Also given: e = (50-20) cm = 30 cm = 0.3 m, k = 350/0.3 N/m
Substitute these values into equation 3
W = 1/2(350/0.3)(0.3²)
W = 350×0.3/2
W = 52.5 J
A closely wound, circular coil with radius 2.80 cm has 790 turns. Part A What must the current in the coil be if the magnetic field at the center of the coil is 0.0760 T
Answer:
[tex]I=11.1A[/tex]
Explanation:
From the question we are told that:
Radius [tex]R=2.80[/tex]
Turns [tex]N=790[/tex]
Magnetic field B=0.0760
Generally the equation for Magnetic field at the center of the coil is mathematically given by
[tex]B=\frac{\mu NI}{2r}[/tex]
[tex]0.076=\frac{4\p*10^-^7*790*I}{2*0.028}[/tex]
[tex]I=\frac{0.076*2*0.028}{4\p*10^{-7}*790}[/tex]
[tex]I=11.1A[/tex]
Determine the amount of work done on an ideal gas as it is heated in an enclosed thermally insulated cylinder topped with a freely moving piston. The cylinder contains of n moles of the gas and the temperature is raised from T1 to T2. The piston has a mass m and a cross sectional area A.
Answer:
W = 3/2 n (T₁- T₂)
Explanation:
Let's use the first law of thermodynamics
ΔE = Q + W
in this case the cylinder is insulated, so there is no heat transfer
ΔE = W
internal energy can be related to the change in temperature
ΔE = 3/2 n K ΔT
we substitute
3/2 n (T₂-T₁) = W
as the work is on the gas it is negative
W = 3/2 n (T₁- T₂)
What did you enjoyed about the webinar?
Explanation:
hjjdjdjjddjjdndnbbhhhydgdhgdgdvgbbb! bbbhhhhhhhhExplain in terms of impulse how padding reduces forces in a collision. State this in terms of a real example, such as the advantages of a carpeted vs. tile floor for a day care cente
Answer:
Impulse = Average force x time of contact
Explanation:
Impulsive force is a force which is very large but applied on a body for a very small duration of time.
Impulse is given by the change in momentum of the body.
Impulse = Average force x small time interval
When padding is there, the time interval of contact is large and thus, the force exerted by the body is small.
So, when a person falls on the tile floor, there is no compression and thus, the time of contact is very small and thus the impulsive force is very large, due to which the body may damage.
So, when a person falls on the carpeted floor, there is a compression and thus, the time of contact is comparatively large and thus the impulsive force is small, due to which the body may safe.
DUE IN 1 MINUTE PLS ANSWER QUICK ...A sound wave moving with a speed of 1500 m/s is sent from a submarine to the ocean floor. It reflects off the
ocean floor and is received 15s later. What is the distance between the submarine and the ocean floor?
Answer:
s = 11250 m = 11.25 km
Explanation:
The distance covered by the sound wave while traveling from submarine to ocean floor and then back to submarine can be given as follows:
[tex]s = vt[/tex]
but, the distance between the floor and the submarine will be half of this value:
[tex]s = \frac{1}{2}vt[/tex]
where,
s = distance between submarine and ocean floor = ?
v = velocity of sound = 1500 m/s
t = time taken for the round trip = 15 s
Therefore,
[tex]s = \frac{1}{2}(1500\ m/s)(15\ s)[/tex]
s = 11250 m = 11.25 km
1.A motor is rated at 1.5 hp. At what speed in m/s can this motor raise a
200 kg load?
2. A bucket of water with a total weight of 50 Newtons is lifted at constant
velocity up a 10 meter deep well. If it takes 20 seconds to raise the bucket
this distance, what is the power required to lift the bucket?
Answer:
1. 0.57 m/s
2. 25 Watts
Explanation:
1. Determination of the speed.
We'll begin by converting 1.5 hp to watt (W). This can be obtained as follow:
1 hp = 745.7 W
Therefore,
1.5 hp = 1.5 hp × 745.7 W / 1 hp
1.5 hp = 1118.55 W
Next, we shall determine the force. This can be obtained as follow:
Mass (m) = 200 Kg
Acceleration due to gravity (g) = 9.8 m/s²
Force (F) =?
F = m × g
F = 200 × 9.8
F = 1960 N
Finally, we shall determine the speed. This can be obtained as follow:
Power (P) = 1118.55 W
Force (F) = 1960 N
Speed (v) =?
P = F × v
1118.55 = 1960 × v
Divide both side by 1960
v = 1118.55 / 1960
v = 0.57 m/s
Thus, the speed is 0.57 m/s
2. Determination of the power.
We'll begin by calculating the velocity. This can be obtained as follow:
Displacement = 10 m up
Time = 20 s
Velocity =?
Velocity = Displacement / time
Velocity = 10 / 20
Velocity = 0.5 m/s
Finally, we shall determine the power. This can be obtained as follow:
Velocity (v) = 0.5 m/s
Force (F) = 50 N
Power (P) =?
P = F × v
P = 50 × 0.5
P = 25 Watts
Therefore, the power required to lift the bucket is 25 Watts
how can you prove that acceleration is a derived unit
a = (dx / dt)²
Explanation: Unit of distance is m (metres) and unit of time is s (seconds) speed v is first derivative of distance x versus time:
v = dx / dt, unit is m/s. Acceleration is second derivative of
speed versus time a = (dx / dt)² = (dv/dt) , unit is m/s²
Answer:
Explanation:
Acceleration is derived unit because it has two fundamental units involved i.e. meter and second square.
The position of a particle at time tt is s(t)=t3+3t.s(t)=t3+3t. Compute the average velocity over the time interval [2,5][2,5] and estimate the instantaneous velocity at t=2.t=2. (Give your answers as whole numbers.)
(a) 42m/s
(b) 15m/s
Explanation:
Given:
The position of a particle at time t
s(t) = t³ + 3t
(i) To compute the average velocity
Average velocity ([tex]V_{avg}[/tex]) is given by the quotient of the change in position and change in time at a given interval of time. i.e
[tex]V_{avg}[/tex] = Δs / Δt
[tex]V_{avg}[/tex] = (s₂ - s₁) / (t₂ - t₁) --------------------(ii)
Given interval of time is [2,5]
Therefore,
t₁ = 2
t₂ = 5
s₁ = position of the particle at t₁.
This is found by substituting t = 2 into equation (i)
s₁ = (2)³ + 3(2)
s₁ = 8 + 6 = 14
s₂ = position of the particle at t₂
This is found by substituting t = 5 into equation (i)
s₂ = (5)³ + 3(5)
s₂ = 125 + 15 = 140
Now, substitute t₁, t₂, s₁ and s₂ into equation (ii) as follows;
[tex]V_{avg}[/tex] = (s₂ - s₁) / (t₂ - t₁)
[tex]V_{avg}[/tex] = (140 - 14) / (5 - 2)
[tex]V_{avg}[/tex] = 126 / 3
[tex]V_{avg}[/tex] = 42
Therefore, the average velocity is 42m/s
(ii) To compute the instantaneous velocity.
The instantaneous velocity is the velocity of the particle at a given instant in time.
The given instant in time is t = 2.
To get the instantaneous velocity (V), differentiate equation (i) with respect to t as follows;
V = [tex]\frac{ds}{dt}[/tex]
V = [tex]\frac{d(t^3 + 3t)}{dt}[/tex]
V = 3t² + 3
Now substitute the value of t = 2 into the above equation
V = 3(2)² + 3
V = 12 + 3
V = 15
Therefore, the instantaneous velocity at t = 2 is 15m/s