Let, after t minutes car catch up with truck.
So, distance covered by car is, d = 200 + 2t.
Acceleration of car is, a = 2 m/s².
Initial velocity, u = 20 m/s.
Now, by equation of motion :
[tex]s =ut+\dfrac{at^2}{2}[/tex]
[tex]200+2t = 20t + \dfrac{2t^2}{2}\\\\t^2+18t -200=0[/tex]
[tex]t=\dfrac{-18\pm\sqrt{18^2-4(1)(-200)}}{2}\\\\t = \dfrac{-18\pm33.53}{2}\\\\t=7.765\ s[/tex]( eliminating negative solution )
Therefore, time required is 7.765 s.
