A car is traveling at a constant negative velocity of 12.0 m/s. The driver steps on the brakes. The car slows to a stop. The car travels 10.0 m while it is slowing down. What is the magnitude of its acceleration? [HINT: Pay attention to direction.]
________m/s2
To find the magnitude of the car's acceleration, we need to use the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
In this case, the car starts with a negative velocity of 12.0 m/s and comes to a stop, so the final velocity is 0 m/s.
Since we are given that the car travels a distance of 10.0 m while it is slowing down, we also need to consider the time it takes to come to a stop.
To find the time, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
We know the distance is 10.0 m, the initial velocity is -12.0 m/s, and the final velocity is 0 m/s.
Plugging these values into the equation, we can solve for time:
10.0 = (-12.0 * time) + (0.5 * acceleration * time^2)
Rearranging the equation and simplifying, we have:
0.5 * acceleration * time^2 - 12.0 * time + 10.0 = 0
Now we have a quadratic equation. We can solve it using the quadratic formula:
time = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 0.5, b = -12.0, and c = 10.0.
Plugging in those values, we can calculate the time it takes for the car to come to a stop.
Once we have the time, we can substitute it back into the acceleration equation to find the magnitude of the acceleration.
So, to recap:
1. Solve the quadratic equation for time using the values given.
2. Substitute the time into the acceleration equation to find the magnitude of the acceleration.