To find the acceleration, angular momentum, torque, and angle of an object subject to a force and moving towards the origin, we need to know the velocity and force vectors of the object.
(a) the acceleration of the objectThe acceleration of the object can be found by taking the derivative of the velocity vector with respect to time. If the object is moving towards the origin, the acceleration vector would be in the opposite direction of the velocity vector.
(b) the angular momentum of the object about the originThe angular momentum of the object about the origin can be found by taking the cross product of the position vector of the object and its velocity vector. The angular momentum is a vector quantity that is perpendicular to both the position and velocity vectors.
(c) the torque about the origin acting on the object(c) The torque about the origin acting on the object can be found by taking the cross product of the position vector of the object and the force vector acting on it. The torque is a vector quantity that is perpendicular to both the position and force vectors.
(d) the angle between the velocity of the object and the force acting on the object.The angle between the velocity of the object and the force acting on it can be found by taking the dot product of the velocity and force vectors and dividing by the magnitudes of both vectors. The angle between the two vectors is measured in radians and can be used to determine how much the force is affecting the velocity of the object.
It's important to note that all these calculations are vector calculations and they are all performed in three-dimensional space and require knowledge of vector calculus and physics.
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Example: A ball rolls off a table 1.5 m high and lands 0.80 m away from the table.
(a) How long will the ball be in the air?
(b) What is the ball's initial horizontal velocity?
(c) What will be the ball's horizontal and vertical velocities when it hits the ground?
Answer:
Below
Explanation:
To fall 1.8 m the time will be found with :
d = 1/2 a t^2
1.5 = 1/2 ( 9.81) t^2 shows t = .55 s
in this .55 s it travels .8 m horizontally
Horizontal velocity = .8 m / .55 s = 1.45 m/s
When it hits the ground , horizontal velocity will still be 1.45 m/s
vertical velocity will be v = at = 9.81 m/s^2 * .55 = 5.42 m/s
A copper rod of length 0.77 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 76 N/m. A magnetic field with a strength of 0.14 T is oriented perpendicular to the surface of the table.
(a) What must be the direction of the current in the copper rod that causes the springs to stretch?
The current flows (left-to-right/right-to-left) in the copper rod.
(b) If the current is 14 A, by how much does each spring stretch?
________ m
Answer:
a) The direction of the current in the copper rod that causes the springs to stretch is left-to-right. This is because the magnetic field is oriented perpendicular to the surface of the table and the force exerted on the rod by the magnetic field is given by F = qVB, where F is the force, q is the charge of the particle, V is the velocity of the particle, and B is the strength of the magnetic field. Since the force is perpendicular to the velocity of the particle, the direction of the current that produces this force must be parallel to the magnetic field. In this case, the magnetic field is oriented perpendicular to the surface of the table, so the current must flow in the direction left-to-right to produce a force that stretches the springs.
b) To find by how much each spring stretches, you can use the formula F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the distance the spring stretches. In this case, the force exerted by the spring is given by F = qVB, and the spring constant is k = 76 N/m. The charge of the particle is q = Ie, where I is the current and e is the charge of an electron. The velocity of the particle is V = L / t, where L is the length of the rod and t is the time it takes the particle to travel the length of the rod. Since the current is 14 A and the length of the rod is 0.77 m, the velocity of the particle is V = 0.77 m / (1 / 14 A) = 10.78 m/s. The strength of the magnetic field is 0.14 T, so the force exerted by the spring is F = (14 A)(1.60 x 10^-19 C)(10.78 m/s)(0.14 T) = 2.40 x 10^-17 N. Therefore, the distance each spring stretches is x = F / k = 2.40 x 10^-17 N / 76 N/m = 3.16 x 10^-19 meters.
According to the law of reflection, what is the relationship between the angle of incidence and the angle of reflection
The law of reflection, The relationship between the angle of incidence and the angle of reflection is that they are equal.
The angle of incidence is the angle between the incoming light ray and the normal line (a line perpendicular to the surface of the reflecting material), and the angle of reflection is the angle between the reflected light ray and the normal line. When a light ray strikes a reflection surface at a certain angle, it will be reflected back at the same angle. This relationship is represented by the equation.
=> angle of incidence = angle of reflection
This relationship holds true for all types of electromagnetic waves and for all surfaces that are reflective, whether they are smooth or rough, opaque or transparent. It's important to note that this is true for regular reflection, which is defined as the reflection of light off a smooth surface. If the surface is rough, the light rays are reflected in many different directions, this is called diffuse reflection.
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For the circuit in the attached plot, find the energy stored in the capacitor under DC conditions. O 30 mJ O 3 mJ O 0.045 mJ O 0.005 mJ
The energy stored in the capacitor is 0.045 mJ. Under DC conditions, the capacitors will be open-circuited.
What is the formula for energy stored in a capacitor?Energy stored in a capacitor can be calculated by
E = ½ CV²
Where
E = energy (J)C = capacitance (F)V = voltage (V)The picture of circuit in the attached plot is in the attachment.
Find the energy stored in the capacitor under DC conditions!
We have
R₁ = 10 ΩR₂ = 20 ΩC = 0.1 μFI = 3 AUnder DC (Direct Current) conditions, the capacitors will be open-circuited. It means that there is no current will flow through the 20 Ω resistor. So, I across the 10 Ω resistor is the same as I source.
See the picture below in the attachment!
The voltage across the 10 Ω resistor is
V = IR
V = 3(10)
V = 30 V
The voltage across the capacitor is the same as the voltage across the 10 Ω resistor.
Vc = V = 30 V
The energy stored would be
E = ½ C Vc²
E = ½ (0.1)(10⁻⁶)(30)²
E = ½ (10⁻⁷)(900)
E = 450 × 10⁻⁷
E = 0.045 × 10⁻³
E = 0.045 mJ
Hence, the energy stored in the capacitor under DC conditions is 0.045 mJ. The correct option is (c).
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Make meaurement and calculation to predict where the puck will land and whether the puck will land on Eintein or not. Upload or decribe all the tep you took to anwer thi. Include the meaurement you made from thi video, the equation you ued and the final reult
In the given case it can be concluded that- The two basic tenets of the special theory of relativity were that observers moving at constant speeds should be subject to the same physical rules and that the speed of light is constant for all observers.
According to Small amounts of mass (m) can be substituted for huge amounts of energy according to the theory, which uses the speed of light to establish the link between energy and matter (E), Einstein's general theory of relativity from 1915, the spacetime curvature is what causes what we experience as the gravitational force.Relativity ushered in the nuclear era while advancing our understanding of elementary particles and their basic interactions in the field of physics. Relativity made it possible for cosmology and astrophysics to predict unusual celestial phenomena like neutron stars, black holes, and gravitational waves.To know more about theory of relativity here
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an object moves 15 meters in 3 seconds. what is its velocity (in m/s)?
Important Formulas:
[tex]v=\dfrac{d}{t}[/tex]
velocity(measured in m/s) = distance(measured in meters) / time(measured in seconds)
__________________________________________________________
Given:
[tex]d=15m[/tex]
[tex]t=3s[/tex]
[tex]v=?[/tex]
__________________________________________________________
Finding velocity:
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{15}{3}[/tex]
__________________________________________________________
[tex]\fbox{v = 5 m/s}[/tex]
The film strip that emerges from the camera is usually a ______________. That is, its color and light values are the opposite of those in the original scene.
The film strip that emerges from the camera is usually a Negative. That is, its color and light values are the opposite of those in the original scene.
What controls how much light enters the camera?One of the three camera settings that affects exposure is the aperture. The shutter speed, aperture, and ISO settings are together referred as as the "exposure triangle." By adjusting the relative amount of light entering a camera lens, an aperture can change the exposure.
What part of the camera and eye controls how much light enters?A camera's shutter can close or open depending on how much light is required to expose the film at the rear of the device.
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You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude
Correct option is C) the acceleration of gravity at that altitude is 9.75m/s².
What is the gravity's acceleration?
The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.
The following formula is used to determine the acceleration of gravity:
g= GM/r2
What G The general gravitational constant is what it is.
G is equal to 6.674x10⁻¹¹ Nm2/kg2, and M is the earth's mass:
M = 5.972x10²⁴kg
The radius of the earth plus the airplane's altitude, or r, is the distance from the earth's center in this case:
r = 6.37x10⁶ m + 20000 m equals 6.39x10⁶ m
Consequently, the acceleration in g is equal to:
(6.674x10⁻¹¹ Nm²/kg²)(5.972x10²⁴ kg) / (6.39x100m)₂
g = 9.75m/s²
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Complete Question -
You are on an airplane traveling with a constant velocity at an altitude of 20,000m. What is the acceleration of gravity at that altitude? The earth's radius is 6.37 x 10^6m.. . A) 9.81 m/s^2. B) 9.78 m/s^2. C) 9.75 m/s^2. D) 9.72 m/s^2. E) 9.69 m/s^2.
The position-time equation of a particle (P) moving in the space reference
system Ox is:
x = 3t? +10t+4 [SI]
1) Specify the nature of motion of (P).
Deduce the values of the acceleration, initial velocity and initial position of
(P).
Write the expression of the velocity of (P) as a function of time. Calculate
its value at t=3s.
Calculate the displacement between t = 2s and t; = 4s.
Which of the following factors affects the strength of the gravitational force between two objects?
Answer: The distance between the objects
Explanation:
Define the following
a. Velocity:
b. Inertia:
c.Speed:
e Force:
f. Balanced force:
g. Net force:
h. Displacement:
Answer:
Explanation:
a.speed with direction associated
b.the ability to resist motion
c.The rate of change of position of an object
e.any influence object's motion
f.forces cancel out, create equilibrium
g.total force acting on an object
h. change in position of an object (total distance from starting point)
PLSS HELP!! Are these True or False questions
Answer:
11. True
12. False (air pressure)
13. False (nitrogen)
14. False (stratosphere)
Explanation:
How do icebergs form in saltwater?
An iceberg is formed by the broken part of a large glacier that floats into the sea. The iceberg is composed of fresh water, just like the glaciers or ice in the North Pole. Since, freshwater is less thick than salty seawater, icebergs float in the water.
When chunks of ice break off the end of a glacier that is flowing into ocean, icebergs are created.
Since, seawater has a slightly higher density than ice, the iceberg floats with the majority of its mass below the surface. A cork, on the other hand, floats quite near to the water's surface due to its density, which is around 20% that of water.
As moving icebergs are dangerous, they have never been a main supply of drinking water. Freshwater is released by melting glaciers and icebergs, which also lowers the salinity of the surrounding sea.
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Two springs have spring constants of 10.0 N/cm and 15.0 N/cm. Which spring is more difficult to stretch
The spring with the higher spring constant (15.0 N/cm) will be more difficult to stretch than the spring with the lower spring constant (10.0 N/cm).
This is because the spring constant is directly related to the amount of force required to stretch the spring. Therefore, the higher the spring constant, the more force that is required to stretch the spring.
The spring constant is a measure of how difficult it is to stretch or compress a spring. It is determined by the stiffness of the spring material, its shape and size, and how much the spring is compressed or stretched.
The higher the spring constant, the more force is required to stretch or compress the spring. The lower the spring constant, the less force is required to stretch or compress the spring.
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The same amount of steel used to create eight solid steel balls, each with a radius of 1 inch, is used to create one larger steel ball. What is the radius of the larger ball
Answer:
2 inches
Explanation:
Volume of a sphere = 4/3 pi r^3
for the EIGHT balls total volume = 8 * 4/3 pi (1^3) = 32/3 pi
This is the volume of the made-up ONE ball
4/3 pi r^3 = 32/3 pi
4/3 r^3 = 32/3
r^3 = 32/3 * 3/4
r^3 = 8
r = 2 inches
A car travels at a constant speed around a circular track whose radius is 3.0 km. The car goes once around the track in 320 s. What is the magnitude of the centripetal acceleration of the car
The magnitude of the centripetal acceleration of the car is 0.0034 km/sec².
What is centripetal acceleration?Centripetal acceleration is the acceleration of an object moving in a circular path. It is directed towards the center of the circle and is responsible for the change in direction of the object's velocity.
The magnitude of the centripetal acceleration of an object moving in a circle is given by the formula:
a = v² / r
where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circle.
Given that the car goes once around the track in 320 s, we can calculate its velocity by using the formula:
v = d / t
where d is the distance traveled and t is the time.
d = 2pir = 2pi3.0 km = 18.849 km
t = 320 sec
so the velocity of the car is v = 18.849 km / 320 sec = 0.059 km/sec.
We can now use the formula to find the centripetal acceleration of the car
a = v² / r = (0.059 km/sec)²/ 3.0 km = 0.0034 km/sec²
Hence, the magnitude of the centripetal acceleration of the car is 0.0034 km/sec².
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600 Joules of work is used to lift a box from the ground to a height of six meters. How much work would have been done if a lever would have been used with an effort arm of 12 meters and a load arm of 6 meters? (10 points)
a. 72 J
b. 100 J
c. 50 J
d. 600 J
Answer:
d. 600 J
Explanation:
You want to know the work done to lift a box using a lever with a mechanical advantage of 2, if the work required without the lever is 600 J.
LeverA lever trades force for distance. That is raising the box a distance of 6 m requires moving the lever arm a distance of 12 m, but only half the force is required. The product of force and distance is the same.
The total required work is unchanged: 600 J.
__
Additional comment
Actually, more work is required to lift the box using the lever. There is work applied to the box, and there is more work applied to moving the lever. (We have to assume a massless lever with no friction in these problems.)
can someone please help me with this i really need this right now thank u ❤️
Answer:
1.constant acceleration.
2.0 ms
3. 0 ms
Explanation:
1. (D) uniformly accelerated motion
2. (A) zero
3. (B) -10 m/s
4. (C) -9.8 m/s^2
5. (B) projectile motion
What is the contribution of hydroelectric power in world electricity?
Hydroelectric power accounts for between 16 and 17 percent of global electricity production, making it one of the most significant renewable energy sources.
In 2016, hydropower contributed more than twice as much to the grid as the next largest renewable energy source, solar. Hydropower can provide many valuable services to the power grid beyond just energy generation. These include frequency regulation, voltage support, contingency reserves, load following, and black start service, all of which contribute to the reliability and safety of the power system. Hydropower's role in grid-scale energy storage, balancing services for other intermittent renewables like wind and solar power, and water management services by reservoirs are growing.
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How are displacements combined?
What is the difference between active and passive flexibility?
The difference between active flexibility and passive flexibility is that in active flexibility, we rely on our own muscle power to reach the end range, but in passive flexibility, we rely on an external push to reach the end range.
According to the findings of recent studies, active flexibility has a stronger connection to a person's level of sporting performance than passive flexibility does. The ability to build active flexibility is more difficult to achieve than passive flexibility. Active flexibility involves passive flexibility in addition to muscle strength in order to be able to retain and maintain the initial extended position.
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A truck was traveling at 24 m/s in came to a stop in 8 seconds. What was the truck's average acceleration over
that time period?
-3 m/s²
2 m/s²
3 m/s²
16 m/s²
Answer:
-3 m/sExplanation:
how I don't know I just guessed but now yall know10 points!
Which measuring tool should be used to measure the length of a marble track?
graduated cylinder
spring scale
metric ruler
stopwatch
Answer:
metric ruler
Explanation:
it counts legnth
Two cells each of EMF 1.5 v and an internal resistance of 2 ohms are connected in parallel. calculate the current flowing when the cells are connected to 1 ohm resistor
Answer:2.30
Explanation:
Which best describes a chemical reaction with accompanying absorption of heat?
Endothermic Reactions
Answer:
Chemical reactions that release energy are called exothermic. ... Chemical reactions that absorb (or use) energy are called endothermic. In endothermic reactions, more energy is absorbed when the bonds in the reactants are broken than is released when new bonds are formed in the products.
Explanation:
Endothermic reactions are ones that absorb heat energy. The excess heat absorbed in the reaction is being used to break bonds in the products. One of the most obvious types of endothermic reaction is the melting of ice. Endothermic Processes
These examples could be written as chemical reactions, but are more generally considered to be endothermic or heat-absorbing processes: Melting ice cubes. Melting solid salts. Evaporating liquid water
A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B. Points A and B are indicated on the string. Orient the two vectors, vA-> and vB-> to correctly represent the direction of the wave velocity at points A and B. rotate the given vectors to indicate the direction of the wave velocity at the indicated points. (Please draw a picture of the end result)
A lengthy string is simple to stretch. The string's two designated spots, A and B, should be at an angle of 90 degrees with the same magnitude, and B should be at an angle of 270 degrees with the same magnitude.
Angle magnitude definition
This is referred to as the amount of rotation that is believed to have been applied to one of the arms' vertex in order to produce a specific position for the other.
It is well known that equal vectors have the same magnitude and direction. When the magnitude and direction of two vectors are the same, they are said to be equal.
|v|=a2+b2 yields the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis.
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The tides are considered an example of shallow-water waves because the tidal bulges have a wavelength that is on the order of __________.
The tides are considered an example of shallow-water waves because the tidal bulges have a wavelength that is on the order of thousands of kilometers.
Which of the aforementioned tide-related claims is true?Complete Response.The tides are caused by the sun and moon's tremendous gravitational pulls on the surface of the planet, which is the right answer.
Which of the following is untrue regarding tides' fundamentals?Response and Justification:Tides are not primarily caused by the gravitational influence of the sun, as is commonly believed.In reality, the Moon's gravitational pull is what mostly causes tides.
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when there is a constant unbalanced force applied in the opposite direction as the motion what will happen to speed and acceleration
Answer:
speed will be constant and so no acceleration
Explanation:
the body will move toward the weaker force, but since the forces are constant there will be no acceleration.
What environmental factors can influence genetic variations?
Some harmful environmental factors can change the nucleotide sequence of a gene. UV rays, for example, can harm DNA strands.
What elements influence genetic variation?Genetic variations arise during meiosis as a result of mutation and recombination. Chemical or biological mutagens frequently result in mutations. The genetic diversity of organisms is also altered by accidental mating.
What are five examples of environmental variations?The length at which you want to wear your hair. Scars – from your own unique accidents. The strength of your muscles depends on how much exercise you get. Piercings, whether you decide to have them or not. Mutations are the primary cause of the emergence of genetic variation.
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The acceleration of a motorcycle is given by ax(t)=At-Bt2,A=1.5m/s2,B=0.120m/s2,the motorcycle at rest at t=0 a)Find its position and velocity as function of time b)What maximum velocity it attains
Answer:
(a)
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex] --- velocity
[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex] --- position
(b) The maximum velocity is: 39.0625m/s
Explanation:
Given
[tex]a_x(t) =At -Bt^2[/tex]
[tex]A = 1.5m/s^3[/tex]
[tex]B = 0.120m/s^4[/tex]
Solving (a): The position and velocity as a function
To calculate the change in velocity, we integrate the given acceleration
i.e.
[tex]\int\limits^{v(t)}_{v(0)} {dv} = \int\limits^t_0 {a(t)} \, dt[/tex]
Integrate
[tex]v|\limits^{v(t)}_{v(0)} = \int\limits^t_0 {a(t)} \, dt[/tex]
Substitute v(t) and v(0) for v
[tex]v(t) - v(0) = \int\limits^t_0 {a(t)} \, dt[/tex]
[tex]v(0) = 0[/tex] ---- The initial velocity.
So, we have:
[tex]v(t) - 0 = \int\limits^t_0 {a(t)} \, dt[/tex]
[tex]v(t) = \int\limits^t_0 {a(t)} \, dt[/tex]
Substitute: [tex]a_x(t) =At -Bt^2[/tex]
[tex]v(t) = \int\limits^t_0 {[At -Bt^2]} \, dt[/tex]
Integrate
[tex]v(t) = {\frac{At^2}{2} -\frac{Bt^3}{3}}|\limits^t_0[/tex]
Substitute 0 and t for t
[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - [\frac{A*0^2}{2} -\frac{B*0^3}{3}][/tex]
[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - 0[/tex]
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
To calculate the change in position, we integrate the calculated velocity
i.e.
[tex]\int\limits^{x(t)}_{x(0)} {dx} = \int\limits^t_0 {v(t)} \, dt[/tex]
Integrate
[tex]x(t)|\limits^{x(t)}_{x(0)} = \int\limits^t_0 {v(t)} \, dt[/tex]
Substitute x(t) and x(0) for x(t)
[tex]x(t) - x(0) = \int\limits^t_0 {v(t)} \, dt[/tex]
Substitute: [tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
[tex]x(t) - x(0) = \int\limits^t_0 {\frac{At^2}{2} -\frac{Bt^3}{3}} \, dt[/tex]
Integrate
[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}}|\limits^t_0[/tex]
Substitute t and 0 for t
[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [\frac{A*0^3}{6} -\frac{B*0^4}{12}][/tex]
[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [0][/tex]
[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}[/tex]
Make x(t) the subject
[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex]
Where x(0) represents the initial position
Solving (b): The maximum velocity
First, we calculate the time at which it attains the maximum height
Set acceleration to 0
[tex]a_x(t) =At -Bt^2[/tex]
[tex]At - Bt^2 = 0[/tex]
Factorize
[tex]t(A - Bt) = 0[/tex]
Split
[tex]t = 0\ or\ A - Bt = 0[/tex]
t can't be 0.
So, we have:
[tex]A - Bt = 0[/tex]
Solve for t
[tex]-Bt = -A[/tex]
[tex]t = \frac{-A}{-B}[/tex]
[tex]t = \frac{A}{B}[/tex]
Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]
[tex]t = \frac{1.5m/s^3}{0.120m/s^4}[/tex]
[tex]t = \frac{1.5}{0.120}s[/tex]
[tex]t = 12.5s[/tex]
Substitute [tex]t = 12.5s[/tex] in v(t) to get the maximum velocity
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
[tex]v(t) = \frac{A*12.5^2}{2} -\frac{B*12.5^3}{3}[/tex]
[tex]v(t) = \frac{156.25A}{2} -\frac{1953.125B}{3}[/tex]
Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]
[tex]vmax = (156.25*1.5)/2 -(1953.125*0.120)/3[/tex]
[tex]v_{max} = 117.1875 - 78.125[/tex]
[tex]v_{max} = 39.0625[/tex]