The displacement x of a particle at time t along a straight line is given by x=a-bt yt×t.the acceleration of the particle is?

Question

Answer

Answer

Answer

The displacement x of a particle at time t along a straight line is given by:

x = a - bt + yt×t

To find the acceleration of the particle, we need to differentiate the displacement equation twice with respect to time (t).

First Derivative:
The first derivative of x with respect to t gives us the velocity v of the particle:

v = dx/dt = -b + y(2t)

Second Derivative:
Taking the second derivative of x with respect to t gives us the acceleration a of the particle:

a = dv/dt = d²x/dt² = d/dt (-b + y(2t))

To differentiate the equation, we need to apply the rules of differentiation. The derivative of a constant is zero, and the derivative of y(2t) is 2y.

Differentiating the equation, we get:

a = 0 + 2y

Therefore, the acceleration of the particle is simply 2y.

Explanation:
- The displacement equation x = a - bt + yt×t represents the position of a particle at any given time t along a straight line.
- To find the acceleration, we need to differentiate the displacement equation twice with respect to time (t).
- The first derivative of x with respect to t gives us the velocity v of the particle, and the second derivative gives us the acceleration a.
- By differentiating the equation, we find that the acceleration is 2y, where y is a constant.
- This means that the particle's acceleration is directly proportional to the constant y, and it does not depend on time or any other variables.

In conclusion, the acceleration of the particle is 2y.

Answer

X=a-bt-yt2
dx/dt=-b-2yt
v=dx/dt=-b-2yt
dv/dt=-2y
a=dv/dt=-2y

Answer

615 sq m

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