Question

the displacement of a particle is given by y=a+bt+ct^3.then find initial velocity and acceleration

Answer 1

Answer

This is testing the concept of differentiation.

Since we are given displacement, we get velocity by differentiating the displacement function.

To get acceleration we differentiate the velocity function.

Velocity :

dy/dt = V

V = b + 2ct - 4dt³

dv/dt = a

a = 2c - 12dt²

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Answer 2

Explanation:

Given,

Displacement of particle is y = a + bt + ct³   --- (1)

To find the velocity at any instant differentiate it with respect to t

v = (dy/dt)

  = d/dt[a + bt + ct³]

  = 0 + b + 3ct

  = b + 3ct

To find velocity at t=0, we put t=0 in equation (2). Then,

v(at t = 0) = b

Now,

The acceleration can be found by differentiating v with respect to t,

a = dv/dt

  = d/dt[b + 3ct]

  = 3ct

The acceleration of the particle is dependent on time.

At t = 0 s, the acceleration is 0.

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