Step 1 :The problem gives us that a car initially going at a speed of 50 ft/sec brakes at a constant rate and comes to a stop in 5 seconds.
Step 2 :This means that the car's velocity decreases linearly from 50 ft/sec to 0 ft/sec over 5 seconds. Therefore, the deceleration rate is \(-10 \, \text{ft/sec}^2\).
Step 3 :We can calculate the distance the car travels by integrating the velocity function over the time interval [0, 5].
Step 4 :Let's denote time as \(t\), velocity as \(v\), and distance as \(d\). We have \(v = 50 - 10t\).
Step 5 :By integrating the velocity function over the time interval [0, 5], we find that \(d = 125\).
Step 6 :So, the car travels \(\boxed{125}\) feet.