Free Version
Difficult

# Kinematics with Calculus: Acceleration as a Function of Velocity

APPHMC-O@VGCG

An unidentified flying object's vertical acceleration is found to vary over time as a function of its vertical velocity, which also varies over time. Its acceleration in $m/s^2$ is given by the equation $a(t)=3+2v$, when $t$ is measured in seconds.

Determine the velocity as a function of time, if the object starts from rest.

A

$v(t)={v}^{2}+\cfrac{3v}{2}$

B

$v(t)=1.5{ e }^{2t }-1.5$

C

$v(t)=2$

D

$v(t)={ e }^{t }-1$

E

$v(t)=\ln \left( t+1 \right)-1$