Answer:
To find the time it took for the car to come to a stop, we need to use the following equation:
v_f^2 = v_0^2 + 2 * a * d
where v_f is the final velocity (0 m/s), v_0 is the initial velocity, a is the acceleration (-5.00 m/s^2), and d is the distance traveled (15.0 m).
Since v_f = 0 m/s, we can simplify the equation:
0 = v_0^2 - 2 * a * d
v_0^2 = 2 * a * d
v_0 = sqrt(2 * a * d)
Next, we can use the value of v_0 to find the time it took to come to a stop:
v_0 = sqrt(2 * a * d)
t = (v_f - v_0) / a
where t is the time it took to come to a stop.
Substituting the values into the equation:
t = (0 - sqrt(2 * (-5.00 m/s^2) * 15.0 m)) / (-5.00 m/s^2)
t = sqrt(30 / 5) / (-5.00)
t = sqrt(6) / (-5.00)
t = 0.7746 / -5.00
t = -0.15493 s
Since time cannot be negative, we will consider the magnitude of the time:
t = abs(-0.15493 s)
t = 0.15493 s
So it took approximately 0.155 seconds for the car to come to a stop.
Step-by-step explanation: