If a tree fall in a forest does it make a sound?

A particle moving along the x-axis has a position given by x = (24t – 2.0t 3 ) m, where t is measured in s. What is the magnitud

Vitek1552 [10]

<h2>The magnitude 24 ( $\dfrac{m}{s^2}$ ) of the acceleration of the particle when the particle is not moving.</h2>

Explanation:

Given,

A particle moving along the x-axis has a position given by

$x=(24t-2.0t^3)$ m ........ (1)

To find, the magnitude ( $\dfrac{m}{s^2}$ ) of the acceleration of the particle when the particle is not moving = ?

Differentiating equation (1) w.r.t, 't', we get

$\dfrac{dx}{dt} =\dfrac{d((24t-2.0t^3))}{dt}$

⇒ $\dfrac{dx}{dt} =24(1)-3(2.0)t^{2} =24-6t^{2}$ ....... (2)

⇒ $24-6t^{2} = 0$

⇒ $t^{2}=2^{2}$

⇒ t = 2 s

Again, differentiating equation (2) w.r.t, 't', we get

$\dfrac{d^2x}{dt^2} =-12t$

Put t = 2, we get

$\dfrac{d^2x}{dt^2} =-12(2)=24$

Thus, the magnitude 24 ( $\dfrac{m}{s^2}$ ) of the acceleration of the particle when the particle is not moving.

3 0

3 years ago

In a nuclear fusion reaction two 2H atoms are combined to produce one 4He.

Mrrafil [7]

Answer:

a)= 0.025602u

b) = 23.848MeV

c) N = 1.546 × 10¹³

Explanation:

The reaction is

²₁H + ²₁H ⇄ ⁴₂H + Q

a) The mass difference is

Δm = 2m(²₁H) - m (⁴₂H)

= 2(2.014102u) - 4.002602u

= 0.025602u

b) Use the Einstein mass energy relation ship

The enegy release is the mass difference times 931.5MeV/U

E = (0.025602) (931.5)

= 23.848MeV

c)

the number of reaction need per seconds is

N = Q/E

= 59W/ 23.848MeV

$= \frac{59}{(23.848 \times 10^6 )(1.6 \times 10^1^9) } \\\\= 1.546 \times 10^1^3$

N = 1.546 × 10¹³

5 0

3 years ago

While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile's acceleration? (Reme

slava [35]

Answer:

Acceleration = -0.75 m/s²

Explanation:

Given the following data;

Initial velocity = 24 m/s

Final velocity = 15 m/s

Time = 12 seconds

To find the acceleration of the automobile;

Acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.

Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

$Acceleration (a) = \frac {final \; velocity - initial \; velocity}{time}$

Substituting into the formula, we have;

$Acceleration = \frac{15 - 24}{12}$

$Acceleration = \frac{-9}{12}$

Acceleration = -0.75 m/s²

Therefore, the automobile is decelerating because its final velocity is lesser than its initial velocity, leading to a negative value.

5 0

2 years ago

A perpetual motion machine can never be built because it is not possible to eliminate

d1i1m1o1n [39]

Answer:

D. Friction

Explanation:

Friction is a force that opposes motion. So a perpetual motion machine can never be built because it is impossible to eliminate frictional force. It can only be reduced

8 0

2 years ago

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be lau

Viktor [21]

Answer:

6.75 seconds

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration = 16 m/s²

g = Acceleration due to gravity = 9.81 m/s²

Let y be the distance the rocket is accelerating

960-y is the distance traveled in free fall

$v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 16\times y+0^2}\\\Rightarrow v^2=32y\ m/s$

In free fall

$v^2-u^2=2g(960-y)\\\Rightarrow 0-32y=2g(960-y)\\\Rightarrow -32y=2\times -9.81(960-y)\\\Rightarrow 960-y=\dfrac{-32}{2\times -9.81}y\\\Rightarrow 960-y=1.63098878695y\\\Rightarrow 960=2.63098878695y\\\Rightarrow y=\dfrac{960}{2.63098878695}\\\Rightarrow y=364.881828749\ m$

The distance the rocket will keep accelerating is 364.881828749 m

After which it will travel 960-364.881828749 = 595.118171251 m in free fall

$s=ut+\frac{1}{2}at^2\\\Rightarrow 364.881828749=0t+\frac{1}{2}\times 16\times t^2\\\Rightarrow t=\sqrt{\frac{364.881828749\times 2}{16}}\\\Rightarrow t=6.75353452598\ s$

The time the rocket is accelerating is 6.75 seconds

5 0

3 years ago