Physics, 28.12.2019 06:31 camila68

Aparticle leaves the origin with an initial velocity and a constant acceleration . when the particle reaches its maximum x coordinate, what are

(a) its velocity,
(b) its position vector?

Answers: 3

Show answers

Answers

Answer from: aria0826

(a)

$\displaystyle \vec v_f=$

(b)

$\displaystyle \vec r=$

Explanation:

Constant Acceleration Motion

This describes a situation where an object is constantly changing its velocity over time, at a constant rate. If we treat the magnitudes as scalars (one fixed direction) then we have the following expression to find the final speed v_f in term of the initial speed v_o , the constant acceleration a and the time t

v_f=v_o+at

The distance the object travels can also be found in terms of the same magnitudes

$\displaystyle x=v_ot+\frac{at^2}{2}$

If the object is moving in a two-dimension space, then all the magintudes are vectors, and the formulas change to

$\vec v_f=\vec v_o+\vec at$

$\displaystyle \vec r=\vec v_ot+\frac{\vec at^2}{2}$

The initial components of $\vec r$ are zero, as indicated in the question, so they are not included in the above formula.

The velocities and acceleration have two components in the x and y coordinates

The question does not clearly specify some conditions of the situation, so we'll assume some minimum facts to make this have sense

Assuming vx_o is positive, if the object will eventually reach a maximum x-coordinate, then the x-component of the acceleration must be negative, so the x-component of the velocity decreases to zero and the object moves back in that direction. The acceleration will be written as

$\vec a=$

Where ax is negative

The velocity can be written in vectorial notation as

$\vec v_f=$

Where vx_o and vy_o are the initial velocity components

We can find the time t_m where the object starts to change its direction in the x-axis by equating the v_f component to zero

vx_o+ax.t_m=0

Solving for t_m

$\displaystyle t_m=\frac{vx_f-vx_o}{a}=\frac{0-vx_o}{ax}$

$\displaystyle t_m=-\frac{vx_o}{ax}$

Since ax is negative, t_m is guaranteed to be positive.

(a)

The velocity can be computed at this specific time as

$\vec v_f=$

Replacing t_m

$\vec v_f=$

Simplifying

$\displaystyle \vec v_f=$

(b)

The postition vector at this specific time will be

$\displaystyle \vec r=\vec v_ot_m+\frac{\vec at_m^2}{2}$

$\displaystyle \vec r=.\left ( -\frac{vx_o}{a} \right )+\frac{.\left ( -\frac{vx_o}{a} \right )^2}{2}$

Operating

$\displaystyle \vec r=+$

Simplifying

$\displaystyle \vec r=$

Note: Assuming vx_o was positive doesn't make our formulas less valid. If vx_o was negative, then ax must be positive

Answer from: Quest

dopamine..

"it was found that some people who were taking the drug l-dopa to raise their levels of dopamine were developing schizophrenic-like symptoms supporting research a strength of the dopamine hypothesis is that there are many studies which have shown support for the neurochemical explanation."

Answer from: Quest

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by mathematical calculations before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of uranus led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Another question on Physics

Physics, 21.06.2019 20:20

Two friends are having a conversation. anna says a satellite in orbit is in freefall because the satellite keeps falling toward earth. tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80 m/2 . who do you agree with and why?

Answers: 1

Answer

Physics, 22.06.2019 07:20

Use the information presented in the graph to answer the questions. which segments show acceleration? which segment indicates that the object is slowing down? what is the velocity of segment b? what is the acceleration of segment b?

Answers: 3

Answer

Physics, 22.06.2019 10:00

Which subatomic particle has a negative charge

Answers: 2

Answer

Physics, 22.06.2019 12:30

Uppose we consider the system of the three capacitors as a single "equivalent" capacitor. given the charges of the three individual capacitors calculated in the previous part, find the total charge qtot for this equivalent capacitor. express your answer in terms of v and c.

Answers: 2

Answer

You know the right answer?

Aparticle leaves the origin with an initial velocity and a constant acceleration . when the particle...

Questions