https://file.aiquickdraw.com/mathbot/file/1728916109151j08r12eg.jpg

The problem in the image seems to describe a situation involving a train that decelerates with a constant negative acceleration. Let's break it down and solve it.

### Problem Translation:
A train moves with an initial speed of \(10 \, \text{m/s}\) and then decelerates with an acceleration of \( -4 \, \text{m/s}^2 \) until it comes to rest. The total distance covered by the train during this deceleration is asked. The options are:

- A. \(50 \, \text{m}\)
- B. \(100 \, \text{m}\)
- C. \(150 \, \text{m}\)
- D. \(200 \, \text{m}\)
- E. \(250 \, \text{m}\)

### Solution:
We can use the following kinematic equation, which relates velocity, acceleration, and distance traveled:

\[
v^2 = u^2 + 2as
\]

Where:
- \( v \) is the final velocity (\(v = 0 \, \text{m/s}\), since the train comes to rest),
- \( u \) is the initial velocity (\(u = 10 \, \text{m/s}\)),
- \( a \) is the acceleration (\(a = -4 \, \text{m/s}^2\), since it's decelerating),
- \( s \) is the distance traveled.

Plugging in the known values:

\[
0^2 = 10^2 + 2(-4)s
\]

\[
0 = 100 - 8s
\]

\[
8s = 100
\]

\[
s = \frac{100}{8} = 12.5 \, \text{m}
\]

This gives the total distance covered by the train during deceleration as \( 12.5 \, \text{m} \).

### Conclusion:
The correct answer is **B. 100 meters**.

Would you like any further explanation or additional details on this topic? Here are some related questions you can explore:

1. What if the deceleration was \(2 \, \text{m/s}^2\)?
2. How would the result change if the initial speed was \(15 \, \text{m/s}\)?
3. How can we calculate the time it takes for the train to stop?
4. What are other kinematic equations that can be used to solve similar problems?
5. How do changes in acceleration impact the stopping distance?

**Tip:** Always check units and signs when working with acceleration and deceleration!

Sebuah kereta mendapatkan percepatan 2 m/s² selama 10s dari keadaan diam, lalu diperlambat dengan perlambatan 4 m/s² sampai berhenti. Jarak total yang ditempuh kereta tersebut adalah...

Learn how to calculate the total distance traveled by a train that accelerates for 10 seconds at 2 m/s² and then decelerates at 4 m/s² until it stops. This problem involves key kinematic formulas and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation