When Maggie applies the brakes of her car,
the car slows uniformly from 15.4 m/s to 0
m/s in 2.19 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 out how far ahead of the stop sign Maggie must apply her brakes in order to stop at the sign, we can use the equation of motion:
\(v^2 = u^2 + 2as\)
Where:
- \(v\) is the final velocity (0 m/s, since the car stops)
- \(u\) is the initial velocity (15.4 m/s)
- \(a\) is the acceleration (which can be found using the equation: \(a = \frac{\Delta v}{\Delta t}\))
- \(s\) is the distance we are trying to find
First, let's calculate the acceleration:
\(\Delta v = v - u = 0 - 15.4 = -15.4 \,m/s\)
\(\Delta t = 2.19 \,s\)
\(a = \frac{\Delta v}{\Delta t} = \frac{-15.4\,m/s}{2.19\,s}\)
Now that we have the acceleration, we can find the distance:
\(0 = (15.4^2) + 2 \cdot a \cdot s\)
Simplifying the equation:
\(0 = 237.16 - 33.68s\)
Rearranging to solve for \(s\):
\(33.68s = 237.16\)
\(s = \frac{237.16}{33.68} \,m\)
Calculating the answer:
\(s = 7.045 \,m\)
Therefore, Maggie must apply her brakes approximately 7.045 meters ahead of the stop sign in order to stop at the sign.