Mechanics: Car approaching traffic lights

Question

A driverless car registers that the traffic lights change to amber 40m ahead. The amber light is a 2s warning before turning red. The car is travelling at 17m/s and can accelerate at 4m/s^2 or brake safely at 8m/s^2. What options does the car have?

Answer 1

Assumming acceleration is constant you can work out how far it would travel when accelerating or decelerating.

For acceleration: Using SUVAT to get: $$v=u+at=25$$ then S=2(17m/s + 25m/s)/2=42 (S=t(u+v)/2) As displacement>40 then car will be able to travel the 40m before the light changes to red

For deceleration: Using SUVAT $S=ut+\frac{1}{2}at^2$ => $$0=4t^2 -17t+40$$ As no real solutions cannot decelerate in time.