Answer:
(a) Luna
(b) Luna
Explanation:
(b)
The final speed can be found by using the third equation of motion:
[tex]2as = v_f^2 - v_i^2\\[/tex]
where,
a = acceleration
s = distance covered
vf = final speed
vi = initial speed
For Angela:
a = 2 m/s²
s = 30 m
vi = 4 m/s
vf = v_fa
therefore,
[tex]2(2\ m/s^2)(30\ m) = (v_{fa})^2 - (4\ m/s)^2\\v_{fa}^2 = 120 m^2/s^2 + 16\ m^2/s^2\\v_{fa} = 11.66\ m/s\\[/tex]
For Luna:
a = 3 m/s²
s = 30 m
vi = 3 m/s
vf = v_fl
therefore,
[tex]2(3\ m/s^2)(30\ m) = (v_{fa})^2 - (3\ m/s)^2\\v_{fa}^2 = 180 m^2/s^2 + 9\ m^2/s^2\\v_{fa} = 13.74\ m/s\\[/tex]
Therefore, Luna will be running faster at the end of the race.
(b)
To calculate the time of completion we will use the first equation of motion:
[tex]v_f = v_i + at[/tex]
FOR ANGELA:
[tex]11.66\ m/s = 4\ m/s + (2\ m/s^2)t_a\\t_a = \frac{7.66\ m/s}{2\ m/s^2}\\\\t_a = 3.83\ s[/tex]
FOR LUNA:
[tex]13.74\ m/s = 3\ m/s + (3\ m/s^2)t_l\\t_l = \frac{10.74\ m/s}{3\ m/s^2}\\\\t_l = 3.58\ s[/tex]
Hence, LUNA finishes the race first.
