Final answer:
To determine the time it takes for a car to stop from a speed of 30.0 m/s with an acceleration of -4.0 m/s², use the kinematic equation v_f = v_i + at. With a final velocity of 0 m/s, the time calculated by rearranging and solving this equation is 7.5 seconds.
Step-by-step explanation:
The student asked how much time it would take for a car traveling at a speed of 30.0 m/s to come to a complete stop if it has an acceleration of -4.0 m/s². To find the time, we can use the kinematic equation that relates initial velocity (v_i), final velocity (v_f), acceleration (a), and time (t): v_f = v_i + at.
Since the car comes to a stop, the final velocity v_f is 0 m/s. The initial velocity v_i is given as 30.0 m/s and the acceleration a is -4.0 m/s² (negative because it's deceleration). Substituting the given values into the equation like so: 0 = 30.0 m/s + (-4.0 m/s²)t.
Solving for time t we get:
0 = 30.0 m/s - 4.0 m/s² * t
t = 30.0 m/s / 4.0 m/s² = 7.5 s
Therefore, it will take the car 7.5 seconds to come to a complete stop.