Answer:
a) Q = 1436 kW
b) P ≈ 776 kW
Explanation:
Let's begin by listing out the given parameters:
T1 = 20 °C, u = 40 m/s, T2 = 820 °C, P = 4.3 kW, m = 2.5 kg/s, T3 = 510 °C, V1 = 40 m/s,
V2 = 40 m/s, V3 = 55 m/s, ṁ = 2.5 kg/s
To solve the question, we make this assumption that the size of the pipe is constant
a) No change in velocity implies that heat added is isochoric
Q = m * C * ΔT
Cv of air at 300 K(≈20 °C) = 0.718
Q = 2.5 * 0.718 * (820 − 20)
Q = 1436 kW
b) P = ṁ * Cp * ΔT + ṁ * (V2² - V3²) ÷ 2000] - Ql
V2² - V3² = 55² - 40² = 1425
ΔT = T2 - T3 = 820 - 510 = 310 °C
Cp of air at 300 K(≠20 °C) = 1.005 kJ/kgK
Ql = 4.3 kW
P = 2.5 * (1.005 * 310) + 2.5 * (1425 ÷ 2000) - 4.3
P = 778.875 + 1.78125 - 4.3 = 776.35625
P ≈ 776 kW
During last year’s diving competition, the divers always pull their
limbs in and curl up their bodies when they do flips. Just before
entering the water, they fully extend their limbs to enter straight down
as shown.
Explain the effect of both actions on their angular velocities and
kinetic energy (support your answer with working). Also explain the
effect on their angular momentum.
Answer:
The divers pull in their limbs and curl up their bodies because doing so decreases their moment of inertia and increases their angular velocity
Explanation:
The conservation of angular momentum states that in a rotational system, the initial angular momentum is equal to the final angular momentum if no torque acts on it.
Angular momentum is equal to the product of the moment of inertia about its axis and the angular velocity
Angular momentum = Iω[tex]\\[/tex]
where I = moment of inertial = mass x [tex]radius^{2}[/tex]
I = m[tex]r^{2}[/tex]
angular momentum = m[tex]r^{2}[/tex]ω
since angular momentum is constant, one can see that decreasing the radius of rotation about the body by curling in the limb will cause the moment of inertia to decrease and the angular velocity to increase.
NB: mass of the body is constant.
A firm wants to determine the amount of frictional torque in their current line of grindstones, so they can redesign them to be more energy efficient. To do this, they ask you to test the best-selling model, which is basically a diskshaped grindstone of mass 2.0 kg and radius 9.90 cm which operates at 720 rev/min. When the power is shut off, you time the grindstone and find it takes 41.9 s for it to stop rotating.
(a) What is the angular acceleration of the grindstone in rad/s^2? (b) What is the frictional torque exerted on the grindstone in N·m?
Answer:
a)- 1.799 rad/sec²
b)- 17.6 x 10ˉ³Nm
Explanation:
ω₀ = 720 rev/min x (1 min/60 sec) x (2π rad / 1 rev) = 24π rad/s
a) Assuming a constant angular acceleration, the formula will be
α = (ωf -ω₀) / t
As final state of the grindstone is at rest, so ωf =0
⇒ α = (0-24π) / 41.9 = - 1.799 rad/sec²
b)Moment of inertia I for a disk about its central axis
I = ½mr²
where m=2kg and radius 'r'= 0.099m
I = ½(2)(0.099²)
I = 9.8 x 10ˉ³ kgm²
Next is to determine the frictional torque exerted on the grindstone, that caused it to stop, applying the rotational equivalent of the Newton's 2nd law:
τ = I α =>(9.8 x 10ˉ³)(- 1.799)
τ = - 17.6 x 10ˉ³Nm
(The negative sign indicates that the frictional torque opposes to the rotation of the grindstone).
I need some help!!!!!!!!!
Answer:
The Object will immediately begin moving toward the left
Explanation:
Because the force of thirteen is greater than ten and applied to the opposite side
The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 - x3, where x1t2 denotes the position at time t of the particle. (a) If a particle is located at x = 1 when t = 2, what is its velocity at this time? (b) Show that the acceleration of a particle is
Answer:
a)V=7 m/s
b)a=3t²-3x² t³ +3 x ⁵
Explanation:
Given that
[tex]\dfrac{dx}{dt}=t^3-x^3[/tex]
a)
We know that velocity V is given as follows
[tex]V=\dfrac{dx}{dt}[/tex]
[tex]V=t^3-x^3[/tex]
At t= 2 s and x= 1 m
[tex]V=2^3-1^3=7 m/s[/tex]
V=7 m/s
b)
Acceleration a is given as follows
[tex]a=\dfrac{dV}{dt}[/tex]
[tex]a=3t^2-3x^2\dfrac{dx}{dt}[/tex]
Now by putting the values
[tex]a=3t^2-3x^2\times (t^3-x^3)[/tex]
a=3t²-3x² t³ +3 x ⁵
Therefore the acceleration of a particle will be 3t²-3x² t³ +3 x ⁵.
A 46.0-kg box is being pushed a distance of 8.80 m across the floor by a force P whose magnitude is 171 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.250. Determine the work done on the box by (a) the applied force, (b) the friction force, (c) the normal force, and (d) by the force of gravity. Be sure to include the proper plus or minus sign for the work done by each force.
Answer:
a) 1504.8 J
b) 991.76 J
c) 0J
d) 0J
Explanation:
(a) The work done by the force P on the box is given by the following formula:
[tex]W_P=Px[/tex]
P: applied force = 171N
x: distance in which the for P is applied = 8.80m
you replace the values of P and x and obtain:
[tex]W_P=(171N)(8.80m)=1504.8J[/tex]
(b) The work don by the friction force is:
[tex]W_f=F_fx=\mu N x=\mu Mg x[/tex]
μ = coefficient of kinetic friction = 0.250
M: mass of the box = 46.0kg
g: gravitational constant = 9.8 m/s^2
[tex]W_f=(0.250)(46.0kg)(9.8m/s^2)(8.80m)=991.76J[/tex]
(c) The Normal force is
[tex]N=Mg=(46.0kg)(9,8m/s^2)=450.8N[/tex]
but this force does not do work on the box because the direction is perpendicular to the direction of the force P.
[tex]W_N=0J[/tex]
(d) the same as before:
[tex]W_g=0J[/tex]
Very large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index ( ), defined as =5/2 . In the expression, is the duration of the accleration, but is not equal to the acceleration. Rather, is a dimensionless constant that equals the number of multiples of that the acceleration is equal to.
In one set of studies of rear-end collisions, a person's velocity increases by 12.1 km/h with an acceleration of 35.0 m/s2 . Let the + direction point in the direction the car is traveling. What is the severity index for the collision?
How far does the person travel during the collision if the car was initially moving forward at 5.80 km/h ?
Answer:
SI = 2.31
d = 0.161 m
Explanation:
First, convert km/h to m/s.
12.1 km/h × (1000 m/km) × (1 h / 3600 s) = 3.36 m/s
Find the time.
v = at + v₀
3.36 = (35.0)t + 0
t = 0.0960
Find the value of a.
a = a / g
a = 35.0 / 9.8
a = 3.57
Solve for SI.
SI = (3.57)^(⁵/₂) (0.0960)
SI = 2.31
Solve for d.
v² = v₀² + 2aΔx
(3.36)² = 0² + 2 (35.0) d
d = 0.161
When a star explodes as a supernova, the expanding gas can pass through the interstellar medium triggering...
A.) an increase in variable star activity
B.) formation of new stars
C.) life to develop
D.) additional supernovas
B. Formation of new stars
A sensor mounted to a cantilever beam indicates beam motion with time. When the beam is deflected and released (step test), the sensor signal indicates that the beam oscillates as an underdamped second-order system with a ringing frequency of 10 rad/s. The maximum displacement amplitudes are measured at three different times corresponding to the 1st, 16th, and 32nd cycles and found to be 17, 9, and 5 mV, respectively. Estimate the damping ratio and natural frequency of the beam based on this measured signal, K
Answer:
The damping ratio= 2.93 × 10^-3 and the natural frequency is 10rad/s
Explanation:
Check attachment
An RV is traveling 60 km/h along a highway at night. A boy sitting near the driver of the RV turns a flashlight on and shines it at another boy at the back end of the RV.
Answer:
300,000,000 and the second question is the same.
Explanation:
Edge
Answer:
What is the speed of the light relative to the boys?
✔ 300,000,000
What is the speed of light relative to a stationary observer on the side of the road?
✔ 300,000,000
Explanation: MARK ME BRAINLIEST CUHZZZZZ DA*N (cant say dam or they gone banned me again)
The graph shows the force and displacement of an object that is being pushed. How much work is done to push the object 0.12m?
Answer:
Work done, W = 0.72 J
Explanation:
From the given graph, it is clear that the force applied is 6 N if the extension is 0.12 m.
Work done is given by :
W = Fx
[tex]W=6\ N\times 0.12\ m\\\\W=0.72\ J[/tex]
So, 0.72 J of work is done to push the object 0.12 m
A bike travels 15.0 km in 45.0 min. Its average speed in km/h is .
The average speed of a bus traveling a distance of 15.0 km in 45.0 min is 20 km/hour.
What is speed?The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar quantity.
The distance travelled by an object in a time interval is divided by the length of the interval to determine its average speed.
Distance travelled by the bike = 15.0 km
Time taken by the object = 45.0 minute = (45.0 ÷ 60) hour = 0.75 hour
Hence, the average speed of the object = distance travelled / time taken
= 15.0 km/0.75 hour
= 20 km/hour,
Therefore, the average speed of a bus traveling a distance of15.0 km in 45.0 min is 20 km/hour.
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Word ProNems:
1. A car goes from 4.47 m/s to 17.9 m/s in 3 seconds.
a. Did this car speed up or slow down?
b. Should your answer be positive or negative? Explain your reasoning.
c. Calculate the acceleration of the car.
Answer:
a:it speed up
b:it should be positive since final
velocity is larger than initial velocity
c:acceleration is approximately 4.5
m/s^2
Explanation:
initial velocity=u=4.47m/s
Final velocity=v=17.9m/s
Time=t=3 seconds
a:the car speed up since the velocity
increased
b:change in velocity is positive
because final velocity is larger than
initial velocity
17.9-4.47=13.43 m/s
c: acceleration=(v-u)/t
acceleration=(17.9-4.47)/3
acceleration=13.43/3
acceleration=4.5 m/s^2
If a car goes from a velocity u to a velocity v, the change in velocity is expressed as;
[tex]\triangle v =v-u[/tex]
Given
final velocity v = 17.9m/s
initial velocity u = 4.47m/s
[tex]\triangle v = 17.9-4.47\\\triangle v =13.43m/s[/tex]
a) Since the change in velocity is a positive value, this shows that the car speeds up.
b) The answer should be positive since the final velocity is greater than the initial velocity.
c) Acceleration is the change in velocity with respect to time
[tex]a=\frac{v-u}{t}\\a=\frac{17.9-4.47}{3} \\a=\frac{13.43}{3}\\a= 4.48m/s^2[/tex]
Hence the acceleration of the car is 4.48m/s²
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Gerry is looking at salt under a powerful microscope and notices a crystalline structure. What can be known about the salt sample that Gerry is looking at?
1. The atoms have spread out from each other.
2.The atoms are sliding past each other.
3.The atoms have no particular pattern
4.The atoms are vibrating in place
Answer:
4.The atoms are vibrating in place
Explanation:
The answer is; The atoms are vibrating in place
We know that, molecules in the crystal have a definite position in the crystal and are bonded to each other by electrostatic forces. However, since the molecules have some energy, they vibrate in their positions. Their energy, however, is not high enough to cause them to overcome the strong bonding (unless the crystal is heated or the atoms are irradiated).
Mr. Dunn drives 64.8km from work at a speed of 48km/h. Mrs. Dunn drives 81.2km from work
at a speed of 58km/h. They both leave work at the same time. Show complete working to secure
full credits. [4]
i. Who arrives home first?
ii. How many minutes later is it before the second person gets home?
iii. A Coyote is chasing its meal (the Road Runner). Unfortunately, the Coyote has difficulty
adjusting to the Road Runner’s speed but we have a good idea of what it is.
plz help me i will mark you as brainliest
Answer:
i) Mr. Dunn arrives to home first.
ii) 3 min
Explanation:
i. To find who arrives first to home you calculate the time, by using the following formula:
[tex]t=\frac{x}{v}[/tex]
x: distance
v: velocity
Mr. Dunn:
[tex]t=\frac{64.8km}{48km/h}=1.35h[/tex]
Mrs. Dunn:
[tex]t=\frac{81.2km}{58km/h}=1.4h[/tex]
Hence, Mr. Dunn arrives to home first.
ii. To calculate the difference in minutes, you convert hours to minutes:
[tex]1.35h*\frac{60min}{1h}=81min\\\\1.40h*\frac{60min}{1h}=84min\\\\\Delta\ t=(84-81)min=3min[/tex]
the difference between the times is 3min
(i) Mr. Dunn takes less time so he arrives at home first.
(ii) The second person arrives 3 min late.
Time taken to arrive home:
(i) We have to calculate the time taken to reach home by Mr. Dunn and Mrs. Dunn.
t = x/v
where x is the distance
and v is the velocity
Time taken by Mr. Dunn:
distance x = 64.8 km
speed v = 48 km/h
t = 64.8 / 48
t = 1.35 h
Time taken by Mrs. Dunn:
distance x = 81.2 km
speed v = 58 km/h
t' = 81.2 / 58
t' = 1.4 h
Hence, Mr. Dunn arrives at home first.
(ii) To calculate the difference in minutes, you convert hours to minutes:
The time taken by Mr. Dunn in minutes is:
t = 1.35×60 = 81 minutes
The time taken by Mrs. Dunn in minutes is:
t' = 1.4×60 = 84 minutes
the difference between the times is 3min
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Which of the following could possibly be predicted? Earthquakes Landslides Foreshocks Volcanic eruptions
Answer:
Volcanic Eruptions
Explanation:
The volcano can start showing signs that it may be about to explode.
Answer:
Volcanic eruptions.
Explanation:
I had the same question on an assignment and I got it right.
A. A PH202 student lives next to a construction site and sees a crane with a wrecking ball demolish the building next door. The wrecking ball swings along the wall between her house and the neighbor’s house. In an effort to determine the length of the cable on the wrecking ball the student builds a pendulum using a random rock and a string. Her pendulum turns out to be 0.500m long. While she plays with her pendulum she realizes that the wrecking ball swings back and forth in the same amount of time that it takes the rock to complete 5 full oscillations. What is the length of the cable on the wrecking ball?
Answer:
The length of cable is 12.5 m
Explanation:
Since, the wrecking ball completes 1 oscillation, in the same time, as it takes for the rock to complete 5 oscillations.
Therefore,
Time Period of Wrecking Ball = 5 (Time Period of Rock)
Since,
Time Period of Pendulum = 2π√(L/g)
Therefore,
2π√(L₁/g) = 5[2π√(L₂/g)]
√L₁ = 5√L₂
Squaring on both sides:
L₁ = 25 L₂
where,
L₁ = Length of Cable = ?
L₂ = Length of string = 0.5 m
Therefore,
L₁ = 25 (0.5 m)
L₁ = 12.5 m
Alan leaves Los Angeles at 8:00 A.M. to drive to San Francisco 400 mi away. He manages to travel at a steady 50 mph in spite of traffic. Beth leaves Los Angeles at 9:00 A.M. and surprisingly manages to also drive at a constant speed, in this case 60 mph. (Knight 2.1) a. Who gets to San Francisco first? (Beth) b. How long does the first to arrive have to wait for the second? (20 minutes)
Answer:
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
Explanation:
let 'd' be distance b/w Los Angeles and San Francisco i.e 400 mi
considering ,
Alan's speed [tex]v_A[/tex]=50mph
Beth's speed [tex]v_B[/tex]=60mph
->For Alan:
The time required [tex]t_A[/tex]= d/[tex]v_A[/tex]= 400/50 => 8h
-> For beth:
The time required [tex]t_B=\frac{d}{v_B} =\frac{400}{60} =>6\frac{2}{3} h[/tex] => 6h 40m
Alan will reach at 8:00 a.m +8h = 4:00p.m.
Beth will reach at 9:00 a.m +6h 40m= 3:40p.m.
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65-g fish at rest just at the surface of the water can expel a 0.30-g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. What is the speed of the archerfish immediately after it expels the drop of water?
(a) 0.0025 m/s
(b) 0.012 m/s
(c) 0.75 m/s
(d) 2.5 m/s.
Answer:
(b) 0.012 m/s
Explanation:
Given that:
mass (m₁) of the drop of water = 0.30 g = 3.0 × 10⁻⁴ kg
mass (M₂) of the fish = 65 g = 65 × 10⁻³ kg
speed (v₁) of the water = 2.5 m/s
speed (v₂) of the archerfish = ??
By conservation of momentum
m₁v₁ - M₂v₂ = 0
m₁v₁ = M₂v₂
v₂ = m₁v₁ / M₂
v₂ = ( 3.0 × 10⁻⁴ × 2.5 ) / 65 × 10⁻³
v₂ = 0.0115 m/s
v₂ ≅ 0.012 m/s
Therefore, the speed of the archerfish immediately after it expels the drop of water 0.012 m/s.
A potato and raisins salad has been warmed up to a temperature of 80∘C and let it stand for three minutes. Then one tries a bite. 1) Would the potatoes and raisins be equally warm? Potatoes have a specific heat of 3430 J/(kg⋅∘C). Raisins have a specific heat of 1630 J/(kg⋅∘C).
Answer:
No. Potatoes will be warmer.
Explanation:
[tex]Q=m\times c\times \Delta T[/tex]
where,
Q = heat taken
m = mass of substance
c = specific heat of substance = ?
ΔT = change in temperature
As we are given that the potatoes have a specific heat of 3430 J/(kg⋅∘C) and raisins have a specific heat of 1630 J/(kg⋅∘C). It implies that substance take more heat when higher the value of specific heat i.e more warmer will be the substance. Thus, the potatoes will be more warmer as compared to raisins.
Therefore, No. Potatoes will be warmer.
I need help plz help me out 10 points!!!!!!!
Answer:
The answer is diffraction
Explanation:
Answer:
The answer is diffraction
Explanation:
I did the test! HOPE THIS HELPS!
You go grab a car door handle in the summer (energy transfer to heat up the handle conduction) and it burns you through _____ energy transfer.
A. Radiation-transfer of energy (heat) through space by electromagnetic rays.
B. Conduction-the transfer of energy (heat) through the matter by molecules energy (touch).
C. Convection-the transfer of heat movement of mass or substance (motion).
I think the answer is A
In this experiment, you need to examine the idea of thermal energy transfer. Using a controlled experiment, what might a good question about the variables that affect thermal energy transfer be? Thermal energy transfer depends on many properties, but limit your question to only two.
Answer:
We shall consider two properties:
1. Temperature difference
2. Thermal conductivity of the material
Use a cylindrical rod of a given material (say steel) which is insulated around its circumference.
One end of the rod is dipped in a large reservoir of water at 100 deg.C and the other end is dipped in water (with known volume) at 40 deg. C. The cold water if stored in a cylinder which is insulated on all sides. A thermometer reads the temperature of the cold water as a function of time.
This experiment will show that
(a) heat flows from a region of high temperature to a region of lower temperature.
(b) The thermal energy of a body increases when heat is added to it, and its temperature will rise.
(c) The thermal conductivity of water determines how quickly its temperature will rise. If mercury replaces water in the cold cylinder, its temperature will rise at a different rate because its thermal conductivity is different.
Explanation:
If Jim could drive a Jetson's flying car at a constant speed of 440 km/hr across oceans and space, approximately how long (in millions of years, in 106 years) would he take to drive to a nearby star that is 12.0 light-years away? Use 9.461 × 1012 km/light-year and 8766 hours per year (365.25 days).
Answer:
t = 2.94 x 10⁶ years
Explanation:
The equation used in the case of constant speed is:
s = vt
t = s/v
where,
s = distance = 12 light years
s = (12 light years)(9.461 x 10¹² km/light year) = 113.532 x 10¹² km
v = speed = 440 km/hr
t = time passed = ?
Therefore,
t = (113.532 x 10¹² km)/(440 km/hr)
t = 2.58 x 10¹¹ hr
Now, converting it to years:
t = (2.58 x 10¹¹ hr)(1 year/8766 hr)
t = 2.94 x 10⁶ years
the medium of a mechanical wave is the matter through wich it travels? tru or false
Answer:
it can only travel through matter
Explanation:
the mechanical wave can be any type of matter
how much force is needed to accelerate a space shuttle 15 m/s2 with a mass of 2,030,000?
Answer:30450000N
Explanation:
Mass=2030000
Acceleration=15 m/s^2
Force=mass x acceleration
Force=2030000 x 15
Force=30450000 N
The force required to accelerate the space shuttle is equal to 3.04 × 10⁷ N.
What is force?Force acting on a body can be described as the influence that can change the state of the body from motion or rest and vice versa. The S.I. unit of force can be denoted as Newton (N) and is a vector parameter.
Force has the ability to change the direction and speed of moving objects. The mathematical expression of the 2nd law of motion for force can be written as:
F = ma
Given the mass of the space shuttle, m = 2030000Kg = 2.03 × 10⁶ Kg
The acceleration of the space shuttle, a= 15 m/s²
The force needed to accelerate a space shuttle by 15 m/s² is equal to:
F = ma = 2.03 × 10⁶ × 15 = 3.04 × 10⁷ N
Therefore, the force needed to accelerate a space shuttle is 3.04 × 10⁷ N.
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Part A - At what angle does it leave?
Part B - At what distance x does it exit the field?
Answer:
Total internal reflection (TIR) is the phenomenon that involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met: the light is in the more dense medium and approaching the less dense medium.
Explanation: Hope i helped!!!
does work done by the electric force depends on the path taken.
Answer:
yes but not sure
Explanation:
i don't know so much but I just guessed I'm not sure
What is the gravitational force related to the distance between two objects?
Answer:
Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases.
answer: It is inversely proportional to the square of the distance.
Explanation:
for the team
) Consider a beam of light traveling from a medium with a low index of refraction n1 to a new medium with a higher index of refraction n2. Use Snell’s Law to explain why total internal reflection will never occur in this situation, regardless of the choice of the incident angle.
Answer:
Snell's law says that
n1*sin(a1) = n2*sin(a2)
n1 < n2
son n2/n1 > 1
then:
sin(a1) = (n2/n1)sin(a2)
the maximum possible value of sin(x) is 1 when x =90°
total internal reflection means that a2= 90°
but as the coefficient that is multiplying sin(a2) is bigger than 1, we can not have a2 = 90°, because the right side will be greater than 1 and the left side can not be bigger than 1, so we can not have a2 = 90°, so we can not have total internal reflection
The maximum possible value of sin(x) is 1 when x =90°total internal reflection means that a2= 90°.
What is snell's law?Snell's law asserts that the ratio of the sines of the angle of incidence 1 and angle of refraction 2 for a given set of media is equal to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, the refractive indices (n2 / n1).
If n1*sin(a1) = n2*sin(a2) and n1 n2 son n2/n1 > 1 according to Snell's law, then:
(n2/n1)sin = sin(a1) (a2)
When x =90°, the maximum feasible value of sin(x) is 1.
Total internal reflection indicates a2=90°, but because the coefficient multiplying sin(a2) is more than 1, we can't have a2 = 90° because the right side will be greater than 1 and the left side will be smaller than 1, therefore we can't have a2 = 90°. so we dont have total reflection.
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The instantaneous speed of a particle moving along one straight line is v(t) = ate−6t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)
Answer:
v_max = (1/6)e^-1 a
Explanation:
You have the following equation for the instantaneous speed of a particle:
[tex]v(t)=ate^{-6t}[/tex] (1)
To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:
[tex]\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))][/tex] (2)
where you have use the derivative of a product.
Next, you equal the expression (2) to zero in order to calculate t:
[tex]a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}[/tex]
For t = 1/6 you obtain the maximum speed.
Then, you replace that value of t in the expression (1):
[tex]v_{max}=a(\frac{1}{6})e^{-6(\frac{1}{6})}=\frac{e^{-1}}{6}a[/tex]
hence, the maximum speed is v_max = ((1/6)e^-1)a
