Which of these is an indication that a chemical reaction has occurred?

At time t=0, a particle is located at the point (3,6,9). It travels in a straight line to the point (5,2,7), has speed 8 at (3,6

Elis [28]

The particle has constant acceleration according to

$\vec a(t)=2\,\vec\imath-4\,\vec\jmath-2\,\vec k$

Its velocity at time $t$ is

$\displaystyle\vec v(t)=\vec v(0)+\int_0^t\vec a(u)\,\mathrm du$

$\vec v(t)=\vec v(0)+(2\,\vec\imath-4\,\vec\jmath-2\,\vec k)t$

$\vec v(t)=(v_{0x}+2t)\,\vec\imath+(v_{0y}-4t)\,\vec\jmath+(v_{0z}-2t)\,\vec k$

Then the particle has position at time $t$ according to

$\displaystyle\vec r(t)=\vec r(0)+\int_0^t\vec v(u)\,\mathrm du$

$\vec r(t)=(3+v_{0x}t+t^2)\,\vec\imath+(6+v_{0y}t-2t^2)\,\vec\jmath+(9+v_{0z}t-t^2)\,\vec k$

At at the point (3, 6, 9), i.e. when $t=0$ , it has speed 8, so that

$\|\vec v(0)\|=8\iff{v_{0x}}^2+{v_{0y}}^2+{v_{0z}}^2=64$

We know that at some time $t=T$ , the particle is at the point (5, 2, 7), which tells us

$\begin{cases}3+v_{0x}T+T^2=5\\6+v_{0y}T-2T^2=2\\9+v_{0z}T-T^2=7\end{cases}\implies\begin{cases}v_{0x}=\dfrac{2-T^2}T\\\\v_{0y}=\dfrac{2T^2-4}T\\\\v_{0z}=\dfrac{T^2-2}T\end{cases}$

and in particular we see that

$v_{0y}=-2v_{0x}$

and

$v_{0z}=-v_{0x}$

Then

${v_{0x}}^2+(-2v_{0x})^2+(-v_{0x})^2=6{v_{0x}}^2=64\implies v_{0x}=\pm\dfrac{4\sqrt6}3$

$\implies v_{0y}=\mp\dfrac{8\sqrt6}3$

$\implies v_{0z}=\mp\dfrac{4\sqrt6}3$

That is, there are two possible initial velocities for which the particle can travel between (3, 6, 9) and (5, 2, 7) with the given acceleration vector and given that it starts with a speed of 8. Then there are two possible solutions for its position vector; one of them is

$\vec r(t)=\left(3+\dfrac{4\sqrt6}3t+t^2\right)\,\vec\imath+\left(6-\dfrac{8\sqrt6}3t-2t^2\right)\,\vec\jmath+\left(9-\dfrac{4\sqrt6}3t-t^2\right)\,\vec k$

4 0

3 years ago

What part of the hammer acts as the fulcrum when the hammer is used to remove a nail

Natali5045456 [20]

The end of it with the dent

6 0

4 years ago

Joe balances a stationary coin on the the tip of his finger 20 cm from the top of the table. How much work is Joe doing?

adell [148]

The work done by Joe is 0 J.

<u>Explanation</u>:

When a force is applied to an object, there will be a movement because of the applied force to a certain distance. This transfer of energy when a force is applied to an object that tends to move the object is known as work done.

The energy is transferred from one state to another and the stored energy is equal to the work done.

W = F . D

where F represents the force in newton,

D represents the distance or displacement of an object.

Force = 0 N, D = 20 cm = 0.20 m

W = 0 $\times$ 0.20 = 0 J.

Hence the work done by Joe is 0 J.

7 0

3 years ago

How is item A different from Item B?

iris [78.8K]

Explanation:

well there is nothing there and it could be different by diffrent objects, idk

8 0

3 years ago

Read 2 more answers

A bomb of mass 4 kg, initially at rest, explodes breaking into two fragments of 1 kg and 3 kg. Which one of the following statem

Kazeer [188]

Answer: The 1 kg fragment will have three times the speed of the 3kg fragment.

Explanation:Here for the bomb, its chemical energy gets converted into the mechanical energy.

According to the law of conservation of momentum, the two bodies will have equal momentum and to satisfy this condition the lighter mass will have the higher velocity.

∵ momentum, p = mass × velocity

∴The 1 kg fragment will have three times the speed of the 3kg fragment.

6 0

4 years ago