Answer:
3.39724 seconds
23.0824792352 m, 101.917520765 m
13.58896 m/s
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
The equation of motion will be
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 125=30\times t+\dfrac{1}{2}\times 4\times t^2\\\Rightarrow 2t^2+30t-125=0\ m[/tex]
[tex]t=\frac{5\left(\sqrt{19}-3\right)}{2},\:t=-\frac{5\left(3+\sqrt{19}\right)}{2}\\\Rightarrow t=3.39724, -18.39724[/tex]
The time at which the cars collide is 3.39724 seconds
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 4\times 3.39724^2\\\Rightarrow s=23.0824792352\ m[/tex]
Car B traveled 23.0824792352 m and Car A traveled 125-23.0824792352 = 101.917520765 m
[tex]v=u+at\\\Rightarrow v=0+4\times 3.39724\\\Rightarrow v=13.58896\ m/s[/tex]
The speed of car B is 13.58896 m/s
