[tex]\\[/tex]
Explanation:
[tex] a_1 \:=\:0.4\:m/s²[/tex]
[tex] t_1 \:=\:60\:s[/tex]
[tex] v_{i1} \:=\:0\:m/s[/tex]
[tex] a_2 \:=\:0\:m/s²[/tex]
[tex] t_2 \:=\:25\:min\:=\:1500\:s[/tex]
[tex] a_3 \:=\:-0.8\:m/s²[/tex]
[tex] v_{f3} \:=\:0\:m/s[/tex]
[tex]\\[/tex]
Distance from Station A to Station B
[tex]\\[/tex]
[tex]a\:=\:\frac{v_f\:-\:v_i}{t}[/tex]
[tex]v_{ave}\:=\:\frac{v_i\:+\:v_f}{2}[/tex]
[tex]v\:=\:\frac{d}{t}[/tex]
[tex]\\[/tex]
Solve for [tex]v_{f1}[/tex]
[tex]a\:=\:\frac{v_f\:-\:v_i}{t}[/tex]
[tex]0.4\:m/s²\:=\:\frac{v_f\:-\:0\:m/s}{60\:s}[/tex]
[tex]24\:m/s\:=\:v_f\:-\:0\:m/s[/tex]
[tex]v_f\:=\:24\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]v_{ave1}[/tex]
[tex]v_{ave}\:=\:\frac{v_i\:+\:v_f}{2}[/tex]
[tex]v_{ave}\:=\:\frac{0\:m/s\:+\:24\:m/s}{2}[/tex]
[tex]v_{ave}\:=\:12\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]d_1[/tex]
[tex]v\:=\:\frac{d}{t}[/tex]
[tex]12\:m/s\:=\:\frac{d}{60\:s}[/tex]
[tex]720\:m\:=\:d[/tex]
[tex]d_1\:=\:720\:m[/tex]
[tex]\\[/tex]
[tex]v_{f1}\:=\:v_{i2}[/tex]
[tex]v_{i2}\:=\:24\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]v_{f2}[/tex]
[tex]a\:=\:\frac{v_f\:-\:v_i}{t}[/tex]
[tex]0\:m/s²\:=\:\frac{v_f\:-\:24\:m/s}{1500\:s}[/tex]
[tex]0\:=\:v_f\:-\:24\:m/s[/tex]
[tex]v_f\:=\:24\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]v_{ave2}[/tex]
[tex]v_{ave}\:=\:\frac{v_i\:+\:v_f}{2}[/tex]
[tex]v_{ave}\:=\:\frac{24\:m/s\:+\:24\:m/s}{2}[/tex]
[tex]v_{ave}\:=\:24\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]d_2[/tex]
[tex]v\:=\:\frac{d}{t}[/tex]
[tex]24\:m/s\:=\:\frac{d}{1500\:s}[/tex]
[tex]36,000\:m\:=\:d[/tex]
[tex]d_2\:=\:36,000\:m[/tex]
[tex]\\[/tex]
[tex]v_{f2}\:=\:v_{i3}[/tex]
[tex]v_{i3}\:=\:24\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]v_{f3}[/tex]
[tex]a\:=\:\frac{v_f\:-\:v_i}{t}[/tex]
[tex]-0.8\:m/s²\:=\:\frac{0\:-\:24\:m/s}{t}[/tex]
[tex](t)(-0.8\:m/s²)\:=\:-24\:m/s[/tex]
[tex]t\:=\:\frac{-24\:m/s}{-0.8\:m/s²}[/tex]
[tex]t\:=\:30\:s[/tex]
[tex]\\[/tex]
Solve for [tex]v_{ave3}[/tex]
[tex]v_{ave}\:=\:\frac{v_i\:+\:v_f}{2}[/tex]
[tex]v_{ave}\:=\:\frac{24\:m/s\:+\:0\:m/s}{2}[/tex]
[tex]v_{ave}\:=\:12\:m/s[/tex]
[tex]\\[/tex]
Solve for [tex]d_3[/tex]
[tex]v\:=\:\frac{d}{t}[/tex]
[tex]12\:m/s\:=\:\frac{d}{30\:s}[/tex]
[tex]360\:m\:=\:d[/tex]
[tex]d_3\:=\:360\:m[/tex]
[tex]\\[/tex]
[tex]d\:= \:d_1\:+\:d_2\:+\:d_3[/tex]
[tex]d\:= \:720\:m\:+\:36,000\:m\:+\:360\:m[/tex]
[tex]d\:= \:37,080\:m[/tex]
[tex]d\:= \:37.08\:km[/tex]
[tex]\\[/tex]
