Question

The displacement s of a particle depends on time t according to the following relation `s = 1/3t^3 - t^2 + t`. The velocity and displacement of the particle at the instant when its acceleration is zero, are respectively ______.

Options

• `0, 1/3`

• `1/3, 0`

• `1/3, 1/3`

• None of the above

Answer 1

The displacement s of a particle depends on time t according to the following relation `s = 1/3t^3 - t^2 + t`. The velocity and displacement of the particle at the instant when its acceleration is zero, are respectively `underlinebb(0, 1/3)`.

Explanation:

`s = 1/3t^3 - t^2 + t`

`v = (ds)/(dt) = (3t^2)/3 - 2t + 1`

a = `(d^2s)/(dt^2)`

= `(6t)/3 - 2 = 0` (given);

t = 1 s

v₁ = 1 - 2 + 1 = 0;

`x_1 = 1/3 - 1 + 1 = 1/3`