# Pebble accelerated by the wind with a starting velocity

• Ursa
In summary, the conversation discusses using differentials to find an equation for displacement and using the quadratic formula to find the time. Then, velocity is calculated using the values obtained from the equation. The resulting velocity is used to find the angle of acceleration using the vector component equation. The factor in the first term is incorrect and the conversation also mentions that there are five standard kinematics equations that use time, displacement, acceleration, initial velocity, and final velocity. The speaker is trying to find the SUVAT equation that uses those four variables.
Ursa
Homework Statement
A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration ##\vec a = (6.0i + 7.0j)m/s^2##. At time t = 0, the velocity is ##(5.0i)m/s## . What are the (a) magnitude and (b) angle of its velocity when it has been displaced by 13.0 m parallel to the x axis?
Relevant Equations
$$x = \frac {-b \pm \sqrt{b^2 -4ac}} {2a}$$
$$V=\sqrt {V_x^2 + V_y^2}$$
$$a_x=a \cos\Theta$$
I first used differentials to find an equation for the displacement.
$$6.0t^2+5.0t=13$$
and using the quadratic formula I got time ##t=1.1##
I then got ##V_x## from ##6.0t+5.0=v_x=11.6##
and ##V_y## from ##7.0t=v_y=7.7##
The I got v from ##V=\sqrt {V_x^2 + Vy^2} ##
$$\sqrt {11.6^2 + 7.7^2} =13.9 m/s$$

Which I took as my velocity.

from there I used the vector vector competent equation ##a_x=a \cos\Theta## to find the angle

##\cos^{-1}\frac {11.6} {13.9}=\Theta=33.4##

Ursa said:
I first used differentials to find an equation for the displacement.
$$6.0t^2+5.0t=13$$
The factor of 6.0 in the first term is not correct. Check the standard kinematics equations for displacement with constant acceleration. Otherwise, your method of solution looks good.

There is no need to find the time.
There are five standard SUVAT equations, each involving four of time, displacement, acceleration, initial velocity, final velocity.
Which three of those are you given, and which are you trying to find? Which SUVAT equation uses just those four?

## 1. What is pebble acceleration?

Pebble acceleration refers to the increase in speed of a pebble as it is moved by the force of wind.

## 2. How is a pebble accelerated by the wind?

A pebble is accelerated by the wind through the transfer of momentum from the moving air molecules to the pebble's surface. This creates a net force on the pebble, causing it to move in the direction of the wind.

## 3. What factors affect the acceleration of a pebble by the wind?

The acceleration of a pebble by the wind is affected by several factors, including the wind speed, the size and shape of the pebble, and the surface roughness of the pebble.

## 4. Does starting velocity affect the acceleration of a pebble by the wind?

Yes, the starting velocity of a pebble can affect its acceleration by the wind. A pebble with a higher starting velocity will experience a greater force from the wind and therefore accelerate faster than a pebble with a lower starting velocity.

## 5. What is the significance of studying pebble acceleration by the wind?

Studying pebble acceleration by the wind can help us better understand the dynamics of wind erosion and the movement of sediment in natural environments. It can also have practical applications, such as in the design of wind-resistant structures or in predicting the dispersal of pollutants by wind.

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