https://file.aiquickdraw.com/mathbot/file/1726976678698bcwys7us.jpg

This question is about two cars with equal mass, applying equal braking force to come to a stop from different initial velocities. Car A has an initial velocity of 12 m/s, while car B has an initial velocity of 30 m/s.

The key concept to apply here is the relationship between the stopping distance, initial velocity, and braking force. 

The stopping distance \( d \) for a vehicle under constant braking force is related to its initial velocity \( v_0 \) and acceleration \( a \) (in this case, negative due to braking) by the equation:

\[
d = \frac{v_0^2}{2a}
\]

Since both cars are applying equal braking force, the deceleration \( a \) is the same for both. Therefore, the stopping distance is proportional to the square of the initial velocity:

\[
d \propto v_0^2
\]

### Ratio of stopping distances:

For Car A:
\[
d_A = \frac{12^2}{2a} = \frac{144}{2a}
\]

For Car B:
\[
d_B = \frac{30^2}{2a} = \frac{900}{2a}
\]

Now, let's find the ratio \( \frac{d_B}{d_A} \):

\[
\frac{d_B}{d_A} = \frac{900}{144} = 6.25
\]

Thus, the stopping distance of Car B is 6.25 times greater than that of Car A.

Answer: The stopping distance of Car A is **less than** that of Car B, and Car B's stopping distance is 6.25 times greater than Car A's.

Would you like further details or clarification?

Here are five related questions for deeper understanding:
1. How does the mass of the cars affect the stopping distance?
2. What happens to the stopping distance if the braking force is not equal for both cars?
3. How would the stopping distance change if the cars were on a slope instead of a flat road?
4. If Car A had an initial velocity of 20 m/s, what would the new ratio of stopping distances be?
5. How does friction between the tires and the road impact stopping distance?

**Tip:** Remember that stopping distance increases with the square of the speed, so even small increases in speed can significantly affect stopping distance.

Two cars of equal mass are going to apply their brakes in order to stop. Car A is traveling at 12 m/s and car B is traveling at 30 m/s. If both cars apply equal braking force in order to stop, how will the stopping distance of car A compare with that of car B? Stopping distance of car A is ______ times greater or less than car B.

Learn how to compare the stopping distances of two cars with equal mass and braking force, traveling at different speeds. This physics problem involves kinematic equations and proportional relationships, making it suitable for high school students (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