When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s 
to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her 
brakes in order to stop at the sign?

To determine how many meters Maggie's car travels before coming to a stop, we can use the equations of uniformly accelerated motion. In this case, the initial velocity, final velocity, and time are given, so we can calculate the distance using the following equation:

\[
d = v_i t + \frac{1}{2} a t^2
\]

Where:
- \( v_i = 15.0 \, \text{m/s} \) is the initial velocity,
- \( v_f = 0.0 \, \text{m/s} \) is the final velocity,
- \( t = 2.50 \, \text{s} \) is the time taken to stop,
- \( a \) is the acceleration (which we can calculate).

### Step 1: Calculate the acceleration
The acceleration \( a \) can be found using the formula:

\[
a = \frac{v_f - v_i}{t}
\]

Substitute the known values:

\[
a = \frac{0.0 \, \text{m/s} - 15.0 \, \text{m/s}}{2.50 \, \text{s}} = -6.0 \, \text{m/s}^2
\]

### Step 2: Calculate the distance
Now that we have the acceleration, we can use the equation for distance:

\[
d = v_i t + \frac{1}{2} a t^2
\]

Substitute the known values:

\[
d = (15.0 \, \text{m/s})(2.50 \, \text{s}) + \frac{1}{2}(-6.0 \, \text{m/s}^2)(2.50 \, \text{s})^2
\]

Now, let’s calculate the distance.The distance Maggie's car travels before coming to a stop is 18.75 meters. Therefore, she must apply her brakes 18.75 meters before the stop sign to stop exactly at the sign.

Do you have any further questions, or would you like more details?

Here are 5 related questions:
1. How can you determine the stopping distance if the initial velocity is doubled?
2. What happens to the stopping distance if the braking time is halved?
3. How would the result change if the car decelerated at a non-uniform rate?
4. What is the car's average velocity during the braking process?
5. How can this concept be applied to real-world driving safety?

**Tip:** Remember that braking distance is proportional to the square of the velocity!

When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes in order to stop at the sign?

Calculate how many meters a car traveling at 15.0 m/s must cover before coming to a stop when it decelerates uniformly in 2.50 seconds. This problem involves key concepts in kinematics, including uniform acceleration and motion in one dimension, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation