An object moves in one dimensional motion with constant acceleration a = 5.3 m/s2.  At time t = 0 s, the object is at x0 = 4.9 m and has an initial velocity of v0 = 3.5 m/s.  

How far will the object move before it achieves a velocity of v = 8.4 m/s?

Your answer should be accurate to the nearest 0.1 m. 

To solve for the distance the object moves before achieving a velocity of \( v = 8.4 \, \text{m/s} \), we can use the following kinematic equation that relates velocity, displacement, and acceleration:

\[
v^2 = v_0^2 + 2a(x - x_0)
\]

Where:
- \( v = 8.4 \, \text{m/s} \) is the final velocity,
- \( v_0 = 3.5 \, \text{m/s} \) is the initial velocity,
- \( a = 5.3 \, \text{m/s}^2 \) is the constant acceleration,
- \( x \) is the final position, and
- \( x_0 = 4.9 \, \text{m} \) is the initial position.

We can rearrange the equation to solve for \( x - x_0 \), which is the distance traveled:

\[
x - x_0 = \frac{v^2 - v_0^2}{2a}
\]

Substitute the given values:

\[
x - x_0 = \frac{(8.4)^2 - (3.5)^2}{2 \times 5.3}
\]

Now let's calculate the distance traveled.

The object will move approximately \( 5.5 \, \text{m} \) before achieving a velocity of \( 8.4 \, \text{m/s} \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the object's velocity after moving an additional 5 meters?
2. How long will it take for the object to reach a velocity of 8.4 m/s?
3. What will the object's position be after reaching a velocity of 8.4 m/s?
4. How far will the object travel if its velocity increases to 12 m/s?
5. What happens to the displacement if the acceleration changes?

**Tip:** When solving kinematics problems, always check if the known values fit the formulas available, such as for motion with constant acceleration.

An object moves in one dimensional motion with constant acceleration a = 5.3 m/s². At time t = 0 s, the object is at x₀ = 4.9 m and has an initial velocity of v₀ = 3.5 m/s. How far will the object move before it achieves a velocity of v = 8.4 m/s?

Learn how to calculate the distance an object moves under constant acceleration. Given acceleration a = 5.3 m/s², initial velocity v₀ = 3.5 m/s, and final velocity v = 8.4 m/s, this problem involves using the kinematic equation to find the distance traveled. Suitable for Grades 10-12.

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