When Maggie applies the brakes of her car,
the car slows uniformly from 15.4 m/s to 0
m/s in 2.41 s.
How far ahead of a stop sign must she apply
her brakes in order to stop at the sign?
Answer in units of m.
To find the distance ahead of the stop sign where Maggie must apply her brakes, we need to use the kinematic equation that relates distance (d), initial velocity (u), final velocity (v), and time (t):
d = ut + (1/2)at^2
In this case:
- Initial velocity (u) = 15.4 m/s
- Final velocity (v) = 0 m/s
- Time (t) = 2.41 s
First, let's find the acceleration (a) using the formula:
a = (v - u) / t
Substituting the values:
a = (0 - 15.4) / 2.41
a ≈ -6.39 m/s^2
Since the car is decelerating, acceleration is negative.
Now, let's substitute the values of u, t, and a into the distance formula:
d = ut + (1/2)at^2
d = 15.4 * 2.41 + (1/2) * (-6.39) * (2.41^2)
d ≈ 37.114 + (-7.996299)
d ≈ 29.1177 m
Therefore, Maggie needs to apply her brakes about 29.1177 meters ahead of the stop sign in order to stop at the sign.