Question

a moving body is covering a distance directly proportional to the square of time find the acceleration of the body ​

Answer 1

Answer:

$\boxed{\mathfrak{Acceleration \ of \ the \ body \ (a) = 2 \ m/s^2}}$

Explanation:

Relation between distance covered with respect to time is given as:

x ∝ t²

x = kt²

k → Proportionality constant

Double differentiation of distance covered w.r.t. time is accelration i.e.

$\rm \implies a = \dfrac{ {d}^{2} x}{d {t}^{2} } \\ \\ \rm \implies a = \dfrac{d}{dt} ( \dfrac{dx}{dt} )\\ \\ \rm \implies a = \dfrac{d }{dt}( \dfrac{d}{dt} ( k{t}^{2})) \\ \\ \rm \implies a = \dfrac{d}{dt} (2kt) \\ \\ \rm \implies a = 2k \: m {s}^{ - 2}$