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The position of a particle is given by the function x=(5t3−8t2+12)m, where t is in s. at what time does the particle reach its minimum velocity?

Answers

Answer 1

Answer:

The particle reach its minimum velocity at time 1.06 sec.

The function is given as

x=5t^3-8t^2+12

Differentiating the above equation with respect to time, to obtain the velocity

dx/dt=v=15t^2-16t

For maximum and minimum values, put dx/dt=0

15t^2-16t=0

On solving the equation, t=0, 1.06

Therefore at time t=1.06 sec, the particle has the minimum value of velocity.

Answer 2

Answer:

The particle reaches its minimum velocity at t = 0 s or t = 16/15 s

Further explanation

Acceleration is rate of change of velocity.

$\large {\boxed {a = (v - u)/(t) } }$

$\large {\boxed {d = (v + u)/(2)~t } }$

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

$x = ( 5t^3 - 8t^2 + 12) ~ m$

To find the velocity function, we will derive the position function above.

$v = (dx)/(dt)$

$v = 5(3)t^(3-1) - 8(2)t^(2-1)$

$v = ( 15t^2 - 16t ) ~ m/s$

Next to calculate the time to reach its minimum speed, then v = 0 m/s

$0 = ( 15t^2 - 16t )$

$0 = t( 15t - 16)$

$\large {\boxed {t = 0 ~s ~ or ~ t = 16/15 ~ s} }$

Learn more

Velocity of Runner : brainly.com/question/3813437
Kinetic Energy : brainly.com/question/692781
Acceleration : brainly.com/question/2283922
The Speed of Car : brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

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What is suedo force.

Answers

What is pseudo force?

A pseudo force, also called a fictitious force or an inertial force, is an apparent force that acts on all bodies whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.

(a) Determine the electric field strength between two parallel conducting plates to see if it will exceed the breakdown strength for air (3 ? 106 V/m). The plates are separated by2.98 mm and a potential difference of 5575 V is applied. (b) How close together can the plates be with this applied voltage without exceeding the breakdown strength?

Answers

Answer:

(a) 1.87×10⁶ V/m

(b) 1.12 mm closer

Explanation:

(a)

Electric Field = Electric potential/distance.

E = V/d ................... Equation 1

Where E = Electric Field, V = Electric potential, d = distance.

Given: V = 5575 V, d = 2.98 mm = 0.00298 m.

Substitute into equation 1

E = 5575/0.00298

E = 1.87×10⁶ V/m

(b)

without exceeding the breakdown strength,

make d the subject of equation 1

d = V/E.............. Equation 2

Given: E = 3×10⁶ V/m, V = 5575 V

Substitute into equation 2

d = 5575/3000000

d = 1.86 mm.

the plate will be = 2.98-1.86 = 1.12 mm closer

The specific heat of substance A is greater than that of substance B. Both A and B are at the same initial temperature when equal amounts of energy are added to them. Assuming no melting or vaporization occurs, which of the following can be concluded about the final temperature TA of substance A and the final temperature TB of substance B?a) TA > TB
b) TA < TB
c) TA = TB
d) More information is needed

Answers

The final temperatures are such that TA > TB.

The specific heat capacity refers to the quantity of heat required to raise the temperature of 1 Kg of a body by 1K. The higher the specific heat capacity of a body, the higher the quantity of heat required to raise the temperature of the body and vice versa.

Hence, if the specific heat of substance A is greater than that of substance B and A and B are at the same initial temperature, when equal amounts of energy are added to them, the final temperature are such that TA > TB.

Learn more: brainly.com/question/1445383

Answer:

$m_A c_(pA) (T_(fA) -T) = m_B c_(pB) (T_(fB)- T)$

For this case, if we try to find the final temperature of A and B, we see that we will obtain an expression in terms of specific heats and masses, from the information given we know the relationship between specific heats, but we don't know the relationship that exists among the masses, then the best option for this case is:

d) More information is needed

(The relation between the masses is not given)

Explanation:

For this case we know the following info:

$c_(pA) > c_(pB)$

Where c means specific heat for the substance A and B.

We also know that the initial temperatures for both sustances are equal:

$T_(iA)= T_(iB)$

We assume that we don't have melting or vaporization in the 2 substances. So we just have presence of sensible heat given by this formula:

$Q = m c_p \Delta T$

And for this case we know that Both A and B are at the same initial temperature when equal amounts of energy are added to them, so then we have this:

$Q_A = Q_B$

And if we replace the formula for sensible heat we got:

$m_A c_(pA) \Delta T_A = m_B c_(pB) \Delta T_B$

And if we replace for the change of the temperature we got:

$m_A c_(pA) (T_(fA) -T_(iA)) = m_B c_(pB) (T_(fB)- T_(iB))$

And since $T_(iA)= T_(iB)= T$ we have this:

$m_A c_(pA) (T_(fA) -T) = m_B c_(pB) (T_(fB)- T)$

d) More information is needed

(The relation between the masses is not given)

In a solution such as salt water, the component that does the dissolving is called the?

Answers

Answer:

Solvent

Explanation:

A solution is a substance that is made by dissolving one component in another.
It is made up of a solvent and a solute.
The component that dissolves the other is known as solvent. Examples of solvents include water, ethanol, milk, chloroform, etc.
The component that dissolves in the other is known as the solute. Examples of solute include salts, sugar, etc.
For example in an aqueous solution of sodium chloride(NaCl); sodium chloride salt is the solute while water is the solvent.

A boy flies a kite with the string at a 30∘ angle to the horizontal. The tension in the string is 4.5 N. Part A Part complete How much work does the string do on the boy if the boy stands still?

Answers

Answer:

Work done is zero

Explanation:

given data

Angle of kite with horizontal = 30 degree

tension in the string = 4.5 N

WE KNOW THAT

Work = force * distance

horizontal force = $Tcos\theta = 4.5*cos30 = 3.89 N$

DISTANCE = 0 as boy stands still. therefore

work done = 3.89 *0 = 0

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