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.