Question

Please help An object is observed to move under the following equation of motion ... x(t) = A√t ... take A =√2. Determine the equations for the velocity and acceleration as a function of time. Write each equation in differential equation format, including second-order, if necessary.

Answer 1

Explanation:

Function of distance w.r.t time :

$x(t) = \: y = \sqrt{2t}$

Differentiate w.r.t time to get velocity :

$\frac{dy}{dt} = v = \frac{1}{ \sqrt{2t} }$

Differentiate w.r.t time to get Acceleration :

$\frac{d^2y}{dx^2} = a \: = - \frac{1}{2t \sqrt{2t} }$