The Velocity $$v ( t ) ( \mathrm { t } ) = x ^ { \prime } ( t )$$

The velocity $$v ( t ) ( \mathrm { t } ) = x ^ { \prime } ( t )$$ at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. $$x ^ { \prime } ( t ) = - 2 ( 5 t + 1 ) ^ { 1 / 2 }$$ ; x(0) = 3
Find:
(a) The position x(t) at time t.
(b) The position of the object at time t = 6.
(c) The time when the object is at x = 2. Round answers for parts (b) and (c) to one decimal place.

A) (a) $x ( t ) = - \frac { 4 } { 15 } ( 5 t + 1 ) ^ { 3 / 2 } + \frac { 49 } { 15 }$
(b) x(6) = -42.8
(c) t = 0.4

B) (a) $x ( t ) = - \frac { 4 } { 15 } ( 5 t + 1 ) ^ { 3 / 2 }$
(b) x(6) = -46.0
(c) t = -0.2

C) (a) $x ( t ) = - \frac { 4 } { 15 } ( 5 t + 1 ) ^ { 3 / 2 } + \frac { 49 } { 15 }$
(b) x(6) = 0.7
(c) t = -6.5

D) (a) $x ( t ) = - \frac { 4 } { 15 } ( 5 t + 1 ) ^ { 3 / 2 }$
(b) x(6) = 1.4
(c) t = -9.7