Answer:
The vector gravitational force is [tex]W = 303.8\ N( -y)[/tex]
Explanation:
From the question we are told that
The mass of the object is [tex]m = 31 \ kg[/tex]
The acceleration due to gravity experienced by the object is [tex]g = 9.8 m/s^2[/tex]
Generally the vector gravitational force on the object is mathematically represented as
[tex]W = 31 * 9.8[/tex]
[tex]W = 303.8\ N (-y)[/tex]
The -y indicates that the direction of the force is towards the center of the earth
What are some of the benefits of learned optimism that have been found in
research?
O
A. Fewer health problems
O
O
B. All of these
C. Making more money
O
D. A lower divorce rate
Answer: fewer health problems
Explanation:
The benefits of learned optimism that have been found in research are Fewer health problems, Making more money, and a lower divorce rate. The correct option is B.
Learned optimism has been associated with numerous benefits in research, including fewer health problems, making more money, and a lower divorce rate. Optimistic people tend to have better physical and mental health, which leads to fewer health problems. Additionally, optimistic people tend to be more successful in their careers and finances, which can lead to higher income and better financial stability. Finally, optimistic people tend to have better relationships, including lower divorce rates, as they are better able to handle conflicts and maintain positive attitudes toward their partners.
In summary, learned optimism has a range of benefits for individuals, including better physical and mental health, greater success in work and education, better relationships with others, and improved resilience. These benefits make learned optimism an important skill for individuals to develop in order to lead happier, healthier, and more successful lives.
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How do most black holes form?
1. A block of metal of mass 2kg is resting on
a frictionless floor. It is struck by a jet
releasing water at the rate of 1kg/sec at a
speed of 5ms-1. What will be the initial
acceleration of the block?
Answer:
The acceleration is [tex]a = 2.5 \ m/s^2[/tex]
Explanation:
From the question we are told that
The mass of the metal block is [tex]m_b = 2 \ kg[/tex]
The mass flow rate of the water is [tex]\r m = 1\ kg/s[/tex]
The speed of the water of the water release is [tex]v_w = 5 m/s[/tex]
Generally according to the law of conservation of linear momentum
[tex]p_i = p_f[/tex]
Now [tex]p_i[/tex] is the initial momentum of the system which mathematically represented as
[tex]p_i = m_w * v_w + m_b * v_b[/tex]
Now [tex]m_w[/tex] is the mass of water at the point of contact with the block which can be deduced as [tex]m_w = 1 \ kg[/tex]
Now since at initial the block is at rest
[tex]v_b = 0 \ m/s[/tex]
So
[tex]p_i = 1 * 5[/tex]
[tex]p_i = 5 \ kgm/ s[/tex]
And [tex]p_f[/tex] is the final momentum of the system which mathematically represented as
[tex]p_f = m_w * v__{fw} } + m_b * v__{fb}}[/tex]
So [tex]v__{fw} }[/tex] is the final velocity of water which is zero due to the fact that when the water hits the block it losses its momentum and eventually the velocity becomes zero
So
[tex]5 = 2 * v__{fb }[/tex]
Thus [tex]v__{fb }} = \frac{5}{2}[/tex]
[tex]v__{fb }} = 2.5 \ m/s[/tex]
Thus
[tex]p_f = 2.5 * 2[/tex]
[tex]p_f = 5 \ kgm /s[/tex]
Now the average momentum change is
[tex]p_a = \frac{p_i +p_f}{2}[/tex]
[tex]p_a = \frac{5+5}{2}[/tex]
[tex]p_a =5 kgm/s[/tex]
Now the force acting on the block is
[tex]F = \frac{p_a }{t}[/tex]
and from the question the initial movement of the block took 1s as it is a mass of water moving at a rate of 1kg/s that caused the first movement of the block
So
[tex]F= \frac{5}{1}[/tex]
[tex]F= 5 \ N[/tex]
Now the acceleration is
[tex]a = \frac{F}{m_b}[/tex]
=> [tex]a = \frac{5}{2}[/tex]
[tex]a = 2.5 \ m/s^2[/tex]
A very light low-friction cyclindrical turntable is mounted on a study base. Although it is balanced, its density may not be uniform. Design an experimental method to gather data that can be used to determine the rotational inertia of the turntable. In each part, provide the explanations and/or diagrams necessary to support your response.
First, list all the equipment you will use and describe what measurements you will take and how you will take them, in enough detail so that another student could carry out your experiment. Use diagrams to clarify your experimental setup.
Answer:
Check the explanation
Explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
The greater the distance between two objects in space, the _______ their gravitational
Answer is Weaker. If it is talking about the objects' gravitational forces.
Time Warner Cable's leadership development program that spanned over 30 days and included weekly videos, practice exercises, and a two hour webinar was discussed in the Sed as an example of which of the following?
a) tracking training through a leaming records store LRS)
b) using big data to analyze training compliance
c) using gamification to enhance learning
d) an application of advances in neuroscience to training
Answer: A.
tracking training through a leaming records store LRS.
Explanation:
An LRS uses xAPI to collect learner data, or experiences, from both online and offline sources. These experiences are reported back to the LRS in the form of xAPI statements, where they are stored. These statements can then be retrieved for reporting and interpretation of the learner data.
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.
The strength of the force of friction depends on which two factors?
Answer:
coefficient of friction (μ) and normal force (N)
Answer: How hard the surfaces push together and the types of surfaces involved
Explanation:
When a switch is closed to complete a DC series RL circuit which has a large time constant, Group of answer choices the electric field in the wires gradually increases to a maximum value. the rate of change of the electric and magnetic fields is greatest at the instant when the switch is closed. all of the above are true. the magnetic field outside the wires gradually increases to a maximum value. only (a) and (c) above are true.
Answer:
The electric and magnetic fields gradually increase.
Explanation:
Time constant in RL circuits, denoted by τ, is equal to the value of L / R which is the value of the inductor over the resistor. It is used to calculate the point when the current will reach the maximum value in the steady state of the circuit. Because of this behavior of the circuit, the magnetic field and the electric field gradually increase to their maximum values.
I hope this answer helps.
John runs 1.0 m/s at first, and then accelerates to 1.6 m/s during
the course of 4.5 seconds. What is his average acceleration (in
m/s2
Answer: [tex]0.13m/s^2[/tex]
Explanation:
[tex]Formula: a=\frac{V_2-V_1}{t}[/tex]
Where;
a = acceleration
V2 = final velocity
V1 = initial velocity
t = time
If John runs 1.0 m/s first, we assume this is V1. He accelerates to 1.6 m/s; this is V2.
[tex]a=\frac{1.6m/s-1.0m/s}{4.5s}[/tex]
[tex]a=\frac{0.6m/s}{4.5s}[/tex]
[tex]a=0.13m/s^2[/tex]
Answer:.13
Explanation:
Refracted light rays...
A- are bent as they pass into a different medium
B- are absorbed by an object
C- are reflected from an object at a variety of angles
D- bounce off a medium
Answer:
A.
Explanation:
Refraction light rays are bent as they pass into a different medium where its speed is different. As refracted light rays pass from a fast medium to a slow medium, the light ray bends toward the normal to the boundary between the two medium. Light refracts as it travels at an angle into a medium with a different refractive index.
what do hydroelectric plants use to generate electrical energy?
Answer:
A. falling water
Explanation:
I got it right on Edgenuity. Good luck on your quiz.
In hydroelectric plants, water falls on turbine and makes it rotate. In generator, this mechanical energy transforms into electrical energy.
What is hydroelectric power?Hydroelectric power is generated by turbines that turn the potential energy of falling or swiftly flowing water into mechanical energy, which is then used to power generators. The most popular renewable energy source in the early 21st century was hydroelectricity, which in 2019 accounted for more than 18% of the world's total power producing capacity.
Water is gathered or stored at a higher elevation during the production of hydroelectric power and then transported through substantial pipes or tunnels (penstocks) to a lower elevation; the difference between these two elevations is referred to as the head. The falling water turns turbines as it nears the bottom of the pipelines. In turn, the turbines power generators, which transfer the mechanical energy of the turbines into electricity.
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A 25 kg rock resting on the bottom of a lake must be moved from the paths of boats. The rock has a density of 2350 kg/m^3. What force is needed to lift the rock while under water?
Answer:
The force needed is the weight of the rock minus the buoyant force.
Explanation:
Two atomic particles approach each other in a head-on collision. Each particle has a mass of 2.97 × 10-25 kg. The speed of each particle is 2.19 × 108 m/s when measured by an observer standing in the laboratory. (a) What is the speed of one particle as seen by the other particle? (b) Determine the relativistic momentum of one particle, as it would be observed by the other.
Answer:
a) [tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]
b) [tex]p=2.81*10^{-16} kg*m/s[/tex]
Explanation:
a) When we have two particles traveling in parallel directions, the formula for relative velocity is:
[tex]\vec{v}_{12}=\frac{\vec{v}_{1}-\vec{v}_{2}}{1-\frac{\vec{v}_{1}\vec{v}_{2}}{c^{2}}}[/tex]
Here we have that v(1) = -v(2), the speed of the of the second particle is the negative of the first one.
If we use these equivalence we have:
[tex]\vec{v}_{12}=\frac{2\vec{v}_{1}}{1+\frac{\vec{v}_{1}^{2}}{c^{2}}}[/tex]
[tex]\vec{v}_{12}=\frac{2*2.19*10^{8}}{1+\frac{2.19*10^{16}}{3*10^{16}}}[/tex]
[tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]
And, [tex]\vec{v}_{21}=-2.86*10^{8} m/s[/tex]
b) The relativistic momentum equation to one particle observed by the other particle, is:
[tex]p=\gamma mv[/tex]
Where gamma is:
[tex]\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]
v is the speed of the first particle relative to the second particle ([tex]2.86*10^{8}[/tex])m is the mass of the particle [tex]2.97*10^{-25} kg[/tex]Then gamma will be:
[tex]\gamma=\frac{1}{\sqrt{1-\frac{(2.86*10^{8})^{2}}{(3*10^{8})^{2}}}}[/tex]
[tex]\gamma=3.31[/tex]
Finally, the value of the momentum will be:
[tex]p=3.31*2.97*10^{-25}*2.86*10^{8}[/tex]
[tex]p=2.81*10^{-16} kg*m/s[/tex]
I hope it helps you!
How does a concave mirror form an image
Answer:
a magnified and erect virtual is found to be formed.
Arm OA rotates counterclockwise with a constant angular velocity of ω = 5 rad/s. As the arm passes the horizontal position, a 6 kg ball is placed at the end of the arm. As the arm moves upward, the ball begins to roll, with negligible rolling resistance, towards the pivot O. It is noted that at θ = 30 ◦ , the ball is 0.9 meters from the pivot and moving towards O along the length of the arm. The ball moves with a speed of 0.4 m/s along the bar. What is the normal force that the arm applies to the ball at this instant? Please, indicate which principle you are applying and explain why.
Answer:
26.92 N
Explanation:
The normal reaction of the ball is due to two force component acting on it.
The normal reaction as a result of the weight of the ballThe normal reaction due to the component of the acceleration of the ball with the rod.However ; the acceleration is in polar coordinate which is given by the relation:
[tex]a^ { ^ \to} = (r- r \omega^2) \hat {e_r} + ( r \theta + 2 r \omega ) \hat {e_ \theta}[/tex]
[tex]a_{\theta} = r \theta + 2 r \omega[/tex]
Given that :
ω = 5 rad/s
mass m = 6 kg
θ = 30 ◦
r = 0.9 m
speed v = 0.4 m/s
[tex]a_{\theta} = 0 + 2(-0.4)*5[/tex]
[tex]a_{\theta}= -4 \ m/s[/tex]
The normal force reaction (N) that the arm applies to the ball at this instant is :
N = mg cos θ + [tex]ma_{\theta}[/tex]
N = (6 × 9.8× cos 30) + (6 ×(-4))
N = 26.92 N
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]
An astronaut visiting Jupiter's satellite Europa leaves a canister of 1.20 mol of nitrogen gas (28.0 g/mol) at 50.0 ∘C on the satellite's surface. Europa has no significant atmosphere, and the acceleration due to gravity at its surface is 1.30 m/s2. The canister springs a leak, allowing molecules to escape from a small hole. Neglect the interaction with surrounding atmosphere. (a) What is the maximum height (in km) above Europa's surface that is reached by a nitrogen molecule whose speed equals the rms speed? Assume that the molecule is shot straight up out of the hole in the canister, and ignore the variation in g with altitude. (b) The escape speed from Europa is 2025 m/s. Can any of the nitrogen molecules escape from Europa and into space?
Answer:
the answer is a
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
g What is a dielectric material? What is a dielectric material? A dielectric material is a material whose relative dielectric constant is not equal 1 A dielectric material is a material which conducts an electric current, assuming normal operating voltages A dielectric material is a material which does not interact with electric field in any way, assuming normal operating voltages A dielectric material is a material through which virtually no current flows, assuming normal operating voltages SubmitRequest Answer Part B Which materials below are dielectric materials
Answer:A dielectric material is a material through which virtually no current flows, assuming normally operating voltage
Explanation:
Dielectric materials are ,which means that no current will flow through them, when a voltage is applied
A 0.009 kg bullet fired through a door enters at 803 m/s and leaves at 617 m/s. If the door material is known to exert an average resistive force of 5620 N on bullets of this type at usual speeds, find the thickness of the door.
Answer:
The thickness of the door is 0.4230 m
Explanation:
Given;
mass of bullet, m = 0.009 kg
initial velocity of the bullet, u = 803 m/s
final velocity of the bullet, v = 617 m/s
average resistive force of the door on the bullet, F = 5620 N
Apply Newton's second law of motion;
Force exerted by the door on the bullet = Force of the moving bullet
F = ma
where;
F is applied force
m is mass
a is acceleration
Also, Force exerted by the door on the bullet = Force of the moving bullet
[tex]F =ma, \ But \ a =\frac{dv}{dt} = \frac{u-v}{t} \\\\F = \frac{m(u-v)}{t}[/tex]
where;
v is the final velocity of the bullet
u is initial velocity of the bullet
t is time
We need to calculate the time spent by the bullet before it passes through the door.
[tex]t = \frac{m(u-v)}{F} \\\\t = \frac{0.009(803-617)}{5620} = 0.0002979 \ s[/tex]
Distance traveled by the bullet within this time period = thickness of the door
This distance is equivalent to the product of average velocity and time
[tex]S = (\frac{u+v}{2}) t[/tex]
where;
s is the distance traveled
[tex]S = (\frac{u+v}{2}) t\\\\S = (\frac{803+617}{2}) 0.0002979\\\\S = 0.4230 \ m[/tex]
Therefore, the thickness of the door is 0.4230 m
A plane electromagnetic wave varies sinusoidally at 90.0 MHz as it travels along the x direction. The peak value of the electric field is 200 V/m, and it is directed along the y direction. Find the wavelength, the period and the maximum value of the magnetic field. Write expressions in SI units for the space and time variations of the electric field and of the magnetic field. Include numerical values, and include subscripts to indicate coordinate directions. Find the average power per unit area that this wave propagates through space.
Answer:
Explanation:
frequency n = 90 x 10⁶ Hz .
time period T = 1 / n
= 1 / 90 x 10⁶
= 1.11 x 10⁻⁸ S.
wavelength = velocity of light / frequency
= 3 x 10⁸ / 90 x 10⁶
= 3.33 m
maximum value of the magnetic field. ( B₀ )
E₀ / B₀ = c where E₀ and B₀ are maximum electric and magnetic field .
E₀ / c= B₀
200/ 3 x 10⁸
= 66.67 x 10⁻⁸ T .
expressions in SI units for the space and time variations of the electric field
[tex]E=E_{0y}sin(2\pi nt - \frac{2\pi x}{\lambda} )[/tex]
[tex]E=200sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )[/tex] N/C
[tex]B=B_{0z}sin(2\pi nt - \frac{2\pi x}{\lambda} )[/tex]
[tex]B=66.67\times 10^{-8}sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )[/tex] T
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!!!
How much water is on the earth
71% of the earth is water
Answer:
hope this helps
Explanation:
71% of earth is water
A light bulb dissipates 100 Watts of power when it is supplied a voltage of 220 volts.
a) What is the current flowing through this light bulb?
b) What is the resistance of the light bulb?
Given Information:
Power = P = 100 Watts
Voltage = V = 220 Volts
Required Information:
a) Current = I = ?
b) Resistance = R = ?
Answer:
a) Current = I = 0.4545 A
b) Resistance = R = 484 Ω
Explanation:
According to the Ohm’s law, the power dissipated in the light bulb is given by
[tex]P = VI[/tex]
Where V is the voltage across the light bulb, I is the current flowing through the light bulb and P is the power dissipated in the light bulb.
Re-arranging the above equation for current I yields,
[tex]I = \frac{P}{V} \\\\I = \frac{100}{220} \\\\I = 0.4545 \: A \\\\[/tex]
Therefore, 0.4545 A current is flowing through the light bulb.
According to the Ohm’s law, the voltage across the light bulb is given by
[tex]V = IR[/tex]
Where V is the voltage across the light bulb, I is the current flowing through the light bulb and R is the resistance of the light bulb.
Re-arranging the above equation for resistance R yields,
[tex]R = \frac{V}{I} \\\\R = \frac{220}{0.4545} \\\\R = 484 \: \Omega[/tex]
Therefore, the resistance of the bulb is 484 Ω
Answer:
bulb will burn out!
Explanation:
Fluorine-18 undergoes beta-plus decay. The child isotope has an atomic mass of
Answer:
18
Explanation:
got it right on edge
Block A, with a mass of 4 kg, is moving with a speed of 2 m/s while Block B, with a mass of 8.4 kg, is moving in the opposite direction with a speed of 6.1 m/s. The center of mass of the two block system is moving with a velocity of ____ m/s. Round your answer to the nearest tenth. Assume Block A is moving in the positive direction.
Answer:
The center of mass move with the velocity of -3.487 m/s.
Explanation:
Given values of block A.
Mass of block A, (M1) = 4 kg
Speed of block A, (V1) = 2 m/s
Given values of block B.
Mass of block B, (M2) = 8.4 kg
Speed of block B, (V2) = -6.1 m/s
Below is the formula to find the velocity of center of mass.
[tex]Velocity = \frac{M1V1 + M2V2}{M1 + M2} \\[/tex]
[tex]= \frac{4 \times 2 + 8.4 \times (-6.1) }{4 + 8.4} \\[/tex]
[tex]= \frac{- 43.24}{12.4}\\[/tex]
[tex]= - 3.487 m/s[/tex]
If you apply a force of 130 N to the lever, how much force is applied to lift the
crate?
Answer:171 N
Explanation:
Answer:
171 N.
Explanation:
Consider a circular vertical loop-the-loop on a roller coaster. A car coasts without power around the loop. Determine the difference between the normal force exerted by the car on a passenger with a mass of mm at the top of the loop and the normal force exerted by the car on her at the bottom of the loop. Express your answer in terms of mmm and the acceleration due to gravity ggg.
Answer:
Explanation:
Let v₁ and v₂ be velocities at lowest and topmost position . Let r be the radius of the circle .
Let N₁ and N₂ be the normal reaction force .
At the top position
centripetal force = N₂ + mg ; so
N₂ + mg = m v₂² / r
At the bottom position
centripetal force = N₁ - mg ; so
N₁ - mg = m v₁² / r
subtracting these two equations
N₁ - mg - N₂ - mg = m v₁² / r - m v₂² / r
N₁ - N₂ - 2mg = 1/r (m v₁² - m v₂² )
N₁ - N₂ - 2mg = 1/r x mg x 2r ( loss of potential energy = gain of kinetic energy )
N₁ - N₂ = 2mg + 2mg
= 4 mg .
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
