Q99
Constant acceleration (SUVAT)
Real-world SUVAT application problem
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You have been hired to synchronize the four traffic lights on an avenue, indicated by the letters O, A, B, and C, as shown in the figure.
The traffic lights are separated by a distance of 500 m. According to statistical data from the traffic control company, a vehicle that is initially stopped at traffic light O typically starts with constant acceleration of $1 \mathrm{~m~s}^{-2}$ until reaching a speed of $72 \mathrm{~km~h}^{-1}$, and from then on, proceeds at constant speed. You must adjust traffic lights A, B, and C so that they change to green when the vehicle is 100 m away from crossing them, so that it does not have to reduce speed at any moment.
Considering these conditions, approximately how long after the opening of traffic light O should traffic lights A, B, and C open, respectively?
(A) $20 \mathrm{~s}, 45 \mathrm{~s}$ and $70 \mathrm{~s}$.
(B) $25 \mathrm{~s}, 50 \mathrm{~s}$ and $75 \mathrm{~s}$.
(C) $28 \mathrm{~s}, 42 \mathrm{~s}$ and $53 \mathrm{~s}$.
(D) $30 \mathrm{~s}, 55 \mathrm{~s}$ and $80 \mathrm{~s}$.
(E) $35 \mathrm{~s}, 60 \mathrm{~s}$ and $85 \mathrm{~s}$.