What is the maximum absolute variation of any periodic function (e.g., a wave) ?

It has been claimed that an insect called the froghopper (Philaenus spumarius) is the best jumper in the animal kingdom. This in

Vladimir [108]

Answer:

v=4m/s

Explanation:

The formulas for accelerated motion are:

$v=v_0+at\\x=x_0+v_0t+\frac{at^2}{2}$

We can derive the formula $v^2=v_0^2+2ad$ from them.

We have:

$v-v_0=at\\t=\frac{v-v_0}{a}$

And substitute:

$x=x_0+v_0(\frac{v-v_0}{a})+\frac{a}{2}(\frac{v-v_0}{a})^2\\x-x_0=\frac{v_0(v-v_0)}{a}+\frac{(v-v_0)^2}{2a}\\2a(x-x_0)=2v_0(v-v_0)+(v-v_0)^2=2v_0v-2v_0^2+v^2+v_0^2-2vv_0=v^2-v_0^2$

Where in the first step of the last row we just multiplied everything by 2a. Since $x-x_0$ is the displacement d, we have proved that $v^2=v_0^2+2ad$

We use then our values to calculate the final velocity when starting from rest, traveling a distance 0.002m with acceleration $4000 m/s^2$ :

$v=\sqrt{v_0^2+2ad}=\sqrt{2(4000m/s^2)(0.002m)}=4m/s$

7 0

3 years ago

A motorboat accelerates uniformly from a velocity of 6.5 m/s west to a velocity of 1.5 m/s west. If its acceleration was 2.7 m/s

expeople1 [14]

Answer:

<em>The motorboat ends up 7.41 meters to the west of the initial position </em>

Explanation:

<u>Accelerated Motion </u>

The accelerated motion describes a situation where an object changes its velocity over time. If the acceleration is constant, then these formulas apply:

$\vec v_f=\vec v_o+\vec a.t$

$\displaystyle \vec r=\vec v_o.t+\frac{\vec a.t^2}{2}$

The problem provides the conditions of the motorboat's motion. The initial velocity is 6.5 m/s west. The final velocity is 1.5 m/s west, and the acceleration is $2.7 m/s^2$ to the east. Since all the movement takes place in one dimension, we can ignore the vectorial notation and work with the signs of the variables, according to a defined positive direction. We'll follow the rule that all the directional magnitudes are positive to the east and negative to the west. Rewriting the formulas:

$v_f=v_o+a.t$

$\displaystyle x=v_o.t+\frac{a.t^2}{2}$

Solving the first one for t

$\displaystyle t=\frac{v_f-v_o}{a}$

We have

$v_o=-6.5,\ v_f=-1.5,\ a=2.7$

Using these values

$\displaystyle t=\frac{-1.5+6.5}{2.7}=1.852\ s$

We now compute x

$\displaystyle x=(-6.5)(1.852)+\frac{(2.7)(1.852)^2}{2}$

$x=-7,41\ m$

The motorboat ends up 7.41 meters to the west of the initial position

5 0

3 years ago

Radio waves from an fm station have a frequency of 103.1 mhz. if the waves travel with a speed of 3.00 ´ 10 m/s, what is the wav

ryzh [129]

The frequency of the radio waves from the fm station is:
$f=103.1 MHz = 103.1 \cdot 10^6 Hz$
And the speed of the waves corresponds to the speed of light:
$v=3 \cdot 10^8 m/s$
Therefore, the wavelength of the radio waves can be found by using the following equation:
$\lambda= \frac{v}{f}= \frac{3 \cdot 10^8 m/s}{103.1 \cdot 10^6 Hz}=2.91 m$

3 0

3 years ago

Which of the following represents a system that is completely open

Softa [21]

The boiling pot of water is completely open

4 0

3 years ago

Read 2 more answers

Holly puts a box into the trunk of her car. Later, she drives around an unbanked curve that has a radius of 48 m. The speed of t

LiRa [457]

Answer:

The minimum coefficient of friction is 0.544