Question

A particle is projected to the right from the position x = 0 with an initial velocity of 9 m/s. If the
acceleration of the particle is defined by the relation 𝑎 = −0.6𝑣
3
2
⁄
, where a and v are expressed
in m/s2
and m/s, respectively, determine (a) the distance the particle will have traveled when its
velocity is 4 m/s, (b) the time when v = 1 m/s, (c) the time required for the particle to travel 6 m.

Answer 1

I have no idea what
3
2
⁄
is about, however
if Vi = 9 m/s and a = -0.6 v
dv/dt=-0.6 v
dv/v =-0.6 dt
v = -(1/.6) ln -.6 t + 9
x = -(1/6) t ln(-.6 t) + t + 9 t = -(1/6) t ln(-.6 t) + 10 t