A particle moves along the x-axis with an initial velocity of 4 m/s and constant acceleration. After 3 seconds, its velocity is 14 m/s. How far did it travel during this interval?

We are given the following information about the motion of the particle:

- Initial velocity \( u = 4 \, \text{m/s} \)
- Final velocity \( v = 14 \, \text{m/s} \)
- Time interval \( t = 3 \, \text{seconds} \)
- Acceleration is constant.

### Step 1: Calculate the acceleration
Using the first equation of motion:

\[
v = u + at
\]
Substituting the known values:

\[
14 = 4 + a(3)
\]

Solve for acceleration \( a \):

\[
14 - 4 = 3a
\]
\[
a = \frac{10}{3} \, \text{m/s}^2
\]

### Step 2: Calculate the distance traveled
Now, use the second equation of motion to find the distance \( s \) traveled during the 3 seconds:

\[
s = ut + \frac{1}{2}at^2
\]
Substitute the known values:

\[
s = 4(3) + \frac{1}{2} \left( \frac{10}{3} \right)(3)^2
\]

Simplify:

\[
s = 12 + \frac{1}{2} \times \frac{10}{3} \times 9
\]
\[
s = 12 + 15
\]
\[
s = 27 \, \text{meters}
\]

Thus, the particle traveled 27 meters during the 3-second interval.

Would you like more details or have any questions?

Here are 5 related questions:
1. What would happen if the acceleration was not constant?
2. How do we calculate the velocity at any specific time during this interval?
3. What is the general formula for displacement in uniformly accelerated motion?
4. How can we graph this motion in terms of velocity versus time?
5. How would the distance change if the initial velocity was negative?

**Tip:** In problems with constant acceleration, you can always use the three basic kinematic equations to find unknown quantities like acceleration, distance, or final velocity.

Learn how to calculate the distance traveled by a particle moving along the x-axis with an initial velocity of 4 m/s and constant acceleration over a time interval of 3 seconds. This detailed solution involves using kinematic equations and is suitable for high school students (Grades 9-12).

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