First, we calculate the distance travelled during the reaction time. The distance travelled is the speed (v) multiplied by the time (t). Here, the speed is 19 m/s and the reaction time is 0.5 seconds. So, the distance travelled during the reaction time (d_t) is 19 m/s * 0.5 s = 9.5 meters.
Second, to find the distance required to stop the car under maximum braking (d_b), we use the physics formula for motion: v_f² = v_i² + 2ad, where v_f is the final velocity, v_i is the initial velocity, a is the acceleration and d is the distance. Here, the final speed is 0 (because the car is stopping), the initial speed is 19 m/s and the acceleration is -10 m/s² (negative because it's deceleration). We rearrange the formula to solve for the distance: 0² = (19 m/s)² + 2 * -10 m/s² * d
This gives us d = -(19 m/s)² / (2 * -10 m/s²) = 18.05 meters.
Lastly, we subtract both the reaction distance and the braking distance from the initial distance to find the final distance between the car and the deer. The initial distance is 35 m, so the final distance (d_f) is 35 m - 9.5 m - 18.05 m = 7.45 meters.
So, when you finally come to a stop, there is about 7.45 meters between your car and the deer.