Answer:
The distance traveled by an object under constant acceleration can be calculated using the equation:
d = v_0 * t + 0.5 * a * t^2
where d is the distance traveled, v_0 is the initial velocity (90 km/hr = 90 * 1000 / 60 / 60 = 25 m/s), t is the time elapsed, and a is the acceleration (-8.0 m/s^2).
First, we need to find the total time elapsed. The reaction time of the driver is 2.5 seconds, so the total time elapsed is:
t = t_r + t_a
t = 2.5 s + (v_f - v_0) / a
where t_r is the reaction time, t_a is the time taken for the car to come to a stop, v_f is the final velocity (0 m/s), and a is the acceleration (-8.0 m/s^2).
To find t_a, we need to solve for the time it takes the car to come to a stop (when v_f = 0 m/s):
0 = v_0 + a * t_a
t_a = -v_0 / a
t_a = -25 m/s / (-8.0 m/s^2) = 3.125 s
So the total time elapsed is:
t = 2.5 s + 3.125 s = 5.625 s
Next, we can use this value for t to find the distance traveled:
d = v_0 * t + 0.5 * a * t^2
d = 25 m/s * 5.625 s + 0.5 * (-8.0 m/s^2) * (5.625 s)^2
d = 141.5625 m
So the car will travel 141.5625 meters before coming to a stop.
Step-by-step explanation: