Have some fr/ee points because i finished highschool today :)

A particle moving along a straight line is subjected to a deceleration ???? = (−2???? 3 ) m/???? 2 , where v is in m/s. If it ha

dlinn [17]

Answer:

(a). The velocity is 0.099 m/s.

(b). The position is 19.75 m.

Explanation:

Given that,

The deceleration is

$a=(-2v^3)\ m/s^2$

We need to calculate the velocity at t = 25 s

The acceleration is the first derivative of velocity of the particle.

$a=\dfrac{dv}{dt}$

$\dfrac{dv}{dt}=-2v^3$

$\dfrac{dv}{-v^3}=2dt$

On integrating

$int{\dfrac{dv}{-v^3}}=\int{2dt}$

$\dfrac{1}{2v^2}=2t+C$

$v^2=\dfrac{1}{4t+2C}$ ....(I)

At t = 0, v = 10 m/s

$10^2=\dfrac{1}{4\times0+2C}$

$C=\dfrac{1}{200}$

Put the value of C in equation (I)

$v^2=\dfrac{1}{4\times25+2\times\dfrac{1}{200}}$

$v=\sqrt{\dfrac{1}{4\times25+2\times\dfrac{1}{200}}}$

$v=0.099\ m/s$

The velocity is 0.099 m/s.

(b). We need to calculate the position at t = 25 sec

The velocity is the first derivative of position of the particle.

$\dfrac{ds}{dt}=v$

On integrating

$\int{ds}=\int(\sqrt{\dfrac{200}{800t+1}})dt$

$s=\dfrac{\sqrt{200}\times2\sqrt{800t+1}}{800}+C'$

At t = 0, s = 15 m

$15=\dfrac{200}{800}+C'$

$C'=15-\dfrac{200}{800}$

$C'=14.75$

Put the value in the equation

$s=\dfrac{\sqrt{200}\times2\sqrt{800\times25+1}}{800}+14.75$

$s=19.75\ m$

The position is 19.75 m.

Hence, (a). The velocity is 0.099 m/s.

(b). The position is 19.75 m.

3 0

3 years ago

The planets Hox and Blox are near each other in the Dorgon system. The Dorgons have very advanced technology, and a Dorgon scien

dexar [7]

<h2>Answer: Decreasing the distance between Hox and Blox, increasing the mass of Hox, or increasing the mass of Hox and Blox. </h2>

Explanation:

According to the law of universal gravitation:

$F=G\frac{m_{1}m_{2}}{r^2}$

Where:

$F$ is the module of the attraction force exerted between both planets

$G$ is the universal gravitation constant.

$m_{1}$ and $m_{2}$ are the masses of both planets.

$r$ is the distance between both planets.

As we can see, the gravity force is directly proportional to the mass of the bodies and inversely proportional to the square of the distance that separates them.

In other words:

If we decrease the distance between both planets (Hox and Blox), the gravitational pull between them will increase.

On the other hand, if we keep the distance between Hox and Blox, but we increase the mass of one of them, or increase the mass of both, the gravitational pull between them will also increase.

7 0

3 years ago

Read 2 more answers

If two charged balloons are 24cm apart and they feel a force of electrical repulsion of 20N, what would the force of electrical

OverLord2011 [107]

Answer:

Soory

Explanation:

I really dont know but i will send you wait

5 0

3 years ago

146,000,000 Express this amount in gigadollars

Tema [17]

I saw an example of yahoo saying that 114,000,000= 0.114, so ima take a guess and say that the way in expressing 146,000,000 in gigadollars would be 0.146. I'm sorry if I am wrong. But if it is right give me a thanks so I could know if I was right or not.

8 0

3 years ago

A kid throws a ball from a tower 45 meters tall how fast is the ball going when it hits the ground?

IRISSAK [1]

Answer:

29.69 m/s

Explanation:

From the question given above, the following data were obtained:

Height (h) = 45 m

Velocity (v) =...?

Next, we shall determine the time taken for the ball to get to the ground. This can be obtained as follow:

Height (h) = 45 m

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) =?

h = ½gt²

45 = ½ × 9.8 × t²

45 = 4.9 × t²

Divide both side by 4.9

t² = 45/4.9

Take the square root of both side

t = √(45/4.9)

t = 3.03 s

Finally, we shall determine the velocity with which the ball hits the ground. This is illustrated below:

Initial velocity (u) = 0 m/s

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) = 3.03 s

Final velocity (v) =.?

v = u + gt

v = 0 + (9.8 × 3.03)

v = 0 + 29.694

v = 29.694 ≈ 29.69 m/s

Therefore, the ball hits the ground with a velocity of 29.69 m/s.

8 0

4 years ago