A 1200 kg car is moving at 33 m/s then has the brakes applied at a deceleration of 6.1 m/s. How far will it move before stopping?
To find the distance the car will move before stopping, we need to determine the time it takes for the car to come to a complete stop. We can then use this time to calculate the distance traveled.
First, let's find the time it takes for the car to stop. We know that the initial velocity (vi) is 33 m/s, the final velocity (vf) is 0 m/s (since the car stops), and the deceleration (a) is -6.1 m/s² (negative because it is decelerating).
We can use the following equation of motion to find the time (t) it takes for the car to stop:
vf = vi + a * t
Since vf is 0 m/s, the equation becomes:
0 = 33 - 6.1 * t
Rearranging the equation to solve for t:
6.1 * t = 33
t = 33 / 6.1
t ≈ 5.4106 seconds
Now that we have the time it takes to stop, we can find the distance traveled (d) using the following equation of motion:
d = vi * t + 0.5 * a * t²
Substituting the given values:
d = 33 * 5.4106 + 0.5 * (-6.1) * (5.4106)²
d ≈ 882.87 meters
Therefore, the car will move approximately 882.87 meters before stopping.