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.

Explanation:

x(t) = A√t

x(t) = √(2t)

v(t) = dx/dt

v(t) = ½ (2t)^-½ × 2

v(t) = (2t)^-½

a(t) = dv/dt

a(t) = -½ (2t)^⁻³/₂ × 2

a(t) = -(2t)^⁻³/₂

the speed of the cart after 3 seconds of low fan speed is ⇒ 54.0 cm/s.

the speed of the cart after 5 seconds of medium fan speed is ⇒ 120.0 cm/s.

the speed of the cart after 2 seconds of high fan speed is ⇒ 64.0 cm/s. 

just did the lab.