Accelerating vehicles question?

Question

I'm having a bit of a brain freeze and can't figure out what equation to begin with for the following question.

A car driving 30.0 m/s hits it's brakes and accelerates at a rate of 2.00 m/s^2 when it sees a car 155 meters ahead traveling at 5.00 m/s. Will the car slow down in time to avoid a collision?

Answer 1

When brakes applied, cars approaching at 30-5 = 25m/s with a separation of 155m

Closing speed is decreasing 2m/s^2

distance(t) = d + v*t + (1/2)a*t^2

= 155 - 25t + 1*t^2

(choose sign <0 for distance decreasing, >0 for distance increasing)

This is a parabola opening up ... need to see if distance <=0 for t>0.  Min of a parabola occurs at t = -b/2a = 25/2

distance(t=25/2) = 155 - 25(25/2) + (25/2)^2

= 155 - 625/2 + 625/4

= 155 - 625/4

= -1.25m

Collision will occur

(I don't know if you are taking calculus, so I didn't use it)