Final answer:
To calculate the distance traveled by the car, use the equation: distance = (initial velocity * time) + (0.5 * acceleration * time^2). Set the distance equal to 0 to find the time it takes for the car to come to a stop. Substitute that value back into the distance equation to find the distance traveled.
Step-by-step explanation:
To calculate the distance traveled by the car, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the initial velocity is 20 m/s, the acceleration is -10 m/s^2, and the car is brought to rest, meaning the final velocity is 0 m/s, we can plug in the values:
distance = (20 * t) + (0.5 * -10 * t^2)
This equation represents the distance traveled as a function of time. To find the time it takes for the car to come to rest, we can set the distance equal to 0:
0 = 20t - 5t^2
This is a quadratic equation that can be solved to find the values of t. The positive solution will give us the time it takes for the car to come to a stop. Substitute that value back into the distance equation to find the distance traveled.