Answer
(a) $t = 354 ~days$
(b) $x = 4.59\times 10^{15}~m$
(c) $x = 0.485~ly$
Work Step by Step
(a) $t = \frac{v-v_0}{a}$
$t = \frac{3.0\times 10^8~m/s-0}{9.80~m/s^2}$
$t = 3.0612\times 10^7~s$
We can convert this time to days:
$t = (3.0612\times 10^7~s)(\frac{1~day}{24\times 3600~s})$
$t = 354 ~days$
(b) $x = (\frac{v+v_0}{2})(t)$
$x = (\frac{3.0\times 10^8~m/s}{2})(3.0612\times 10^7~s)$
$x = 4.59\times 10^{15}~m$
(c) We can find the number of meters in one light year:
$1~ly = (3.0\times 10^8~m/s)(365\times 24\times 3600~s)$
$1~ly = 9.46\times 10^{15}~m$
We can express the answer in part (b) as a fraction of a light year;
$x = \frac{4.59\times 10^{15}~m}{9.46\times 10^{15}~m}$
$x = 0.485~ly$
