https://file.aiquickdraw.com/mathbot/file/1726852833796mh69ctsz.jpg

Let's solve this kinematics problem step by step.

### Given Data:
- Distance between stations X and Y: 2.05 km = 2050 m
- Train A accelerates from rest with an acceleration \( a = 1 \, \text{m/s}^2 \) for \( t = 10 \, \text{s} \), and then continues at a uniform velocity.
- Train B travels at a constant velocity of \( 20 \, \text{m/s} \) towards station X.

#### a) **Calculate the maximum speed that train A reaches after the first 10 s.**

For Train A, we use the equation of motion for velocity under constant acceleration:

\[
v_f = v_i + at
\]
Where:
- \( v_i = 0 \, \text{m/s} \) (initial velocity since the train starts from rest),
- \( a = 1 \, \text{m/s}^2 \) (acceleration),
- \( t = 10 \, \text{s} \).

Thus,

\[
v_f = 0 + (1 \times 10) = 10 \, \text{m/s}.
\]

The maximum speed of Train A after 10 seconds is **10 m/s**.

---

#### b) **Determine the distance that train A covered during the first 10 s.**

To calculate the distance traveled by Train A during the acceleration phase, we use the equation of motion:

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

Substituting the values:

\[
s = 0 + \frac{1}{2} (1) (10^2) = \frac{1}{2} \times 100 = 50 \, \text{m}.
\]

So, Train A covers **50 meters** during the first 10 seconds.

---

#### c) **Determine the distance that train B covered during the first 10 s.**

Since Train B is traveling at a constant velocity of 20 m/s, the distance covered by Train B in 10 seconds is:

\[
s = vt
\]

\[
s = 20 \times 10 = 200 \, \text{m}.
\]

So, Train B covers **200 meters** during the first 10 seconds.

---

#### d) **How long will it take the two trains to pass each other?**

The initial distance between the two trains is 2.05 km = 2050 m. After 10 seconds:
- Train A has traveled 50 m,
- Train B has traveled 200 m.

The remaining distance between them after the first 10 seconds is:

\[
\text{Remaining distance} = 2050 - (50 + 200) = 1800 \, \text{m}.
\]

At this point, both trains are moving at constant velocities:
- Train A at 10 m/s,
- Train B at 20 m/s.

The relative speed between them is:

\[
\text{Relative speed} = 10 + 20 = 30 \, \text{m/s}.
\]

The time taken for the two trains to pass each other is:

\[
t = \frac{\text{Remaining distance}}{\text{Relative speed}} = \frac{1800}{30} = 60 \, \text{seconds}.
\]

So, it will take **60 seconds** for the two trains to pass each other after the first 10 seconds.

---

### Summary:
a) Maximum speed of Train A after 10 seconds: **10 m/s**.  
b) Distance covered by Train A in the first 10 seconds: **50 meters**.  
c) Distance covered by Train B in the first 10 seconds: **200 meters**.  
d) Time for the trains to pass each other after 10 seconds: **60 seconds**.

Would you like further clarifications or detailed explanations on any step?

---

**Related Questions:**
1. What is the total distance covered by Train A by the time it passes Train B?
2. What would happen if Train A had an acceleration of 2 m/s² instead of 1 m/s²?
3. What would the time taken to pass be if Train B slowed down to 15 m/s after the first 10 seconds?
4. How would the time change if Train A decelerated after reaching its maximum velocity?
5. What would be the effect on the time if the distance between stations X and Y increased by 1 km?

**Tip:** Always ensure that the units are consistent when solving kinematics problems—especially between meters and kilometers, or seconds and hours!

Two railway stations are 2.05 km apart. Train A travels from rest from station X and accelerates uniformly at 1 m/s² for 10 s in the direction of station Y. After the 10 s, Train A then travels further at a uniform velocity. At the same time that A departs, Train B travels at a uniform velocity of 20 m/s towards station X. Train B maintains this velocity. a) Calculate the maximum speed that train A reaches after the first 10 s. b) Determine the distance that train A covered during the first 10 s. c) Determine the distance that train B covered during the first 10 s. d) How long will it take the two trains to pass each other?

Solve a Grade 11 kinematics problem where two trains pass each other. Train A accelerates from rest at 1 m/s² for 10 seconds, while Train B travels at a constant speed of 20 m/s. Learn how to calculate maximum speed, distance covered, and time taken for the trains to pass.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation