Help with a physics problem?

Question

A driver traveling at 59 km/h sees a chicken dash out onto the road and slams on the brakes. Accelerating at -7 m/s2, the car stops just in time 24.0 m down the road. What was the driver's reaction time (i.e., the time that elapsed before he engaged the brake)?

It's the last problem of my homework, and I just want to be done. Help appreciated!

Answer 1

let t represent the reaction time

59km/hr = 295/18 m/s

during the reaction time, the driver covers:
d = (295/18)t
d = 295t/18

so now 24 - 295t/18 is the distance away from the chicken the driver is at.

Vf² = 2ad + Vi²

the final velocity of the driver is 0m/s because he stops
0² = 2(-7)(24 - 295t/18) + (295/18)²
-(295/18)² = -14(24 - 295t/18)
[-(295/18)² / -14] = 24 - 295t/18
[ -(295/18)² / -14) - 24 = -295t/18
-295t/18 = -4.8145
t =~ 0.294s

hope this helps