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

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Answers

answered: 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

answered: Guest

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation:

answered: Guest

its c i just checked it

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