First compute the resultant force F:



Then use Newton's second law to determine the acceleration vector
for the particle:



Let
and
denote the particle's position and velocity vectors, respectively.
(a) Use the fundamental theorem of calculus. The particle starts at rest, so
. Then the particle's velocity vector at <em>t</em> = 10.4 s is



If you don't know calculus, then just use the formula,

So, for instance, the velocity vector at <em>t</em> = 10.4 s has <em>x</em>-component

(b) Compute the angle
for
:

so that the particle is moving at an angle of about 313º counterclockwise from the positive <em>x</em> axis.
(c) We can find the velocity at any time <em>t</em> by generalizing the integral in part (a):


Then using the fundamental theorem of calculus again, we have

where
is the particle's initial position. So we get



So over the first 10.4 s, the particle is displaced by the vector

or a net distance of about 395 m away from its starting position, in the same direction as found in part (b).
(d) See part (c).
Fish swimming forward in the water, the water gets pushed backward because the fish moving forward is forcing the water to move backward, the motion forward and backward are the same, they are opposite and equal.
Answer:
Velocity=14[m/s]
Explanation:
We can solve this problem by using the principle of energy conservation, where potential energy becomes kinetic energy.
In the attached image we can see the illustration of the ball falling from the height of 20 meters, at this time the potential energy will have the following value.
![Ep=m*g*h\\where:\\m=3[kg]\\h=20[m]\\](https://tex.z-dn.net/?f=Ep%3Dm%2Ag%2Ah%5C%5Cwhere%3A%5C%5Cm%3D3%5Bkg%5D%5C%5Ch%3D20%5Bm%5D%5C%5C)
![Ep=3*9.81*20\\Ep=588.6[J]](https://tex.z-dn.net/?f=Ep%3D3%2A9.81%2A20%5C%5CEp%3D588.6%5BJ%5D)
When the ball passes through half of the distance (10m) its potential energy will have decreased by half as shown below.
![Ep=3*9.81*10\\Ep=294.3[m]](https://tex.z-dn.net/?f=Ep%3D3%2A9.81%2A10%5C%5CEp%3D294.3%5Bm%5D)
If we know that potential energy is transformed into kinetic energy, we can find the value of speed.
![Ek=\frac{1}{2} *m*v^{2} \\therefore\\v=\sqrt{\frac{Ek*2}{m} } \\v=\sqrt{\frac{294.3*2}{3} } \\\\v=14[m/s]](https://tex.z-dn.net/?f=Ek%3D%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%5C%5Ctherefore%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7BEk%2A2%7D%7Bm%7D%20%7D%20%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B294.3%2A2%7D%7B3%7D%20%7D%20%5C%5C%5C%5Cv%3D14%5Bm%2Fs%5D)
C.even though there is almost no material in the interstellar medium, but do transfer energy.
Explanation:
Light waves travels through space even though there is almost no material in the interstellar medium but do transfer energy.
A wave is any disturbance that transmits energy from one place to another.
- Light is a form of wave which belongs to the electromagnetic spectrum.
- They are propagated transverse to their source of energy.
- These electromagnetic waves are special types of waves.
- They are distinct because they do not require a material medium for their propagation unlike other waves.
- In the interstellar medium. a vacuum is in place.
- There are no matter that can be used for propagating waves.
- Light waves still passes through because they do not require any medium to propagate.
learn more:
Electromagnetic waves brainly.com/question/12450147
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