A particle moves along with x-axis.The position x of particle with respect to time t from origin is given by x=bₒ+b₁t+b₂t².The acceleration of particle is

Options

(a) bₒ
(b) b₁
(c) b₂
(d) 2b₂

Correct Answer:

2b₂

Explanation:

Given, x=b₀+b₁t+b₂t²
Also, v=dx/dt=d/dt(b₀+b₁t+b₂t²)
Using (d/dx).xⁿ=nxⁿ⁻¹, we have
v=b₁+2b₂t
The Acceleration is,
a=dv/dt=d/dt(b₁+2b₂t)
=2b₂

Another Explanation:
Distance , x = b₀ + b₁t + b₂t²
velocity , v = (dx / dt ) = b₁ + 2b₂t
Acceleration, α = d²x / dt² = 2 b₂.