Relation between displacement x and time t is x = 2 – 5t + 6t², the initial velocity will be:

Concept Used:

Velocity (v): The rate of change of displacement with respect to time.

Acceleration (a): The rate of change of velocity with respect to time.

The velocity of a particle is given by:

v = dx/dt

The acceleration of a particle is given by:

a = dv/dt

Calculation:

Given,

Displacement, x = 2 - 5t + 6t²

Velocity is obtained by differentiating displacement with respect to time:

⇒ v = dx/dt = d(2 - 5t + 6t²)/dt

⇒ v = -5 + 12t

Initial velocity is calculated by substituting t = 0:

⇒ v(0) = -5 + 12(0)

⇒ v(0) = -5 m/s

∴ The correct answer is -5 m/s.