An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$. The position is given as a function of time by:
(1) $\left( \frac { 9 P } { 8 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$
(2) $\left( \frac { 8 P } { 9 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 2 } { 3 } }$
(3) $\left( \frac { 9 m } { 8 P } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$
(4) $\left( \frac { 8 P } { 9 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$