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

Multiple Choice

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. $x ^ { t } ( t ) = - 3 ( 3 t + 1 ) ^ { 1 / 2 }$ ; x(0) = 4
Find:
(a) The position x(t) at time t.
(b) The position of the object at time t = 1.
(c) The time when the object is at x = 2.Round answers for parts (b) and (c) to one decimal place.

A) (a) $x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 }$
(b) x(1) = -5.3
(c) t = -0.3

B) (a) $x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 } + \frac { 14 } { 3 }$
(b) x(1) = 0.7
(c) t = -7.7

C) (a) $x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 }$
(b) x(1) = 0.1
(c) t = -12.3

D) (a) $x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 } + \frac { 14 } { 3 }$
(b) x(1) = -0.7
(c) t = 0.5