A particle moves a distance x in time t according to equation x = (t + 5)⁻¹. The acceleration of particle is proportional to

Options

(a) (velocity)^3/2
(b) (distance)^2
(c) (distance) ^ –2
(d) (velocity) ^ 2/3

Correct Answer:

(velocity)^3/2

Explanation:

x = 1 / t + 5
v = dx / dt = -1 / (t + 5)²
a = d²x / dt² = 2 / (t + 5)³ = 2x³
Now, 1 / (t + 5) ∞ v½
1 / (t + 5)³ ∞ v³/² ∞ a