Velocity as a function of position
The given function for velocity is V = √(p1 - p2x), where p1 and p2 are positive constants. This equation represents the velocity of a particle as a function of its position.

Understanding the equation
To understand the equation, let's break it down:

- p1 is a constant that represents the maximum velocity of the particle.
- p2 is a constant that determines the rate at which the velocity decreases with respect to the position x.
- x is the position of the particle.

Acceleration of the particle
Acceleration is the rate of change of velocity with respect to time. To find the acceleration, we need to differentiate the velocity function with respect to time.

Differentiating the velocity function
To differentiate the function V = √(p1 - p2x), we need to use the chain rule. The chain rule states that if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx.

In this case, let's consider u = p1 - p2x and y = √u.

Step 1: Find dy/du
To find dy/du, we differentiate y = √u with respect to u.
dy/du = (1/2) * (u)^(-1/2) = 1 / (2√u)

Step 2: Find du/dx
To find du/dx, we differentiate u = p1 - p2x with respect to x.
du/dx = -p2

Step 3: Find dy/dx
Using the chain rule, dy/dx = dy/du * du/dx
dy/dx = (1 / (2√u)) * (-p2)
dy/dx = -p2 / (2√u)

Acceleration equation
The final result is the derivative of velocity with respect to time, which is dy/dx.
Therefore, the acceleration of the particle is given by the equation:
a = -p2 / (2√(p1 - p2x))

Summary
The acceleration of the particle, given the velocity function V = √(p1 - p2x), is represented by the equation a = -p2 / (2√(p1 - p2x)). This equation relates the acceleration to the constants p1 and p2, as well as the position x of the particle.

A=dv/dt=(dv/ds)vI think ans is xp2^2-p2√p1