A car travels along a straight horizontal road between two sets of traffic lights that are 1200 metres apart.
The car starts from rest at the first set of lights and accelerates uniformly at 2 m s−2^{-2}−2 until it reaches a speed of V V\,V m s−1^{-1}−1.
The car then travels at the constant speed V V\,V m s−1^{-1}−1, before decelerating uniformly at 2 m s−2^{-2}−2 to come to rest at the second set of lights.
The total time for the journey is 70 seconds.
Show that V2−140V+2400=0V^2 - 140V + 2400 = 0V2−140V+2400=0.
Hence find the value of VVV, explaining why the other root of the equation must be rejected.