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To determine the time at which the object changes direction, we need to find when its velocity \( v \) becomes zero, as a change in direction occurs when the object momentarily stops moving in one direction before reversing.

Given:
\[
v = (4.2 \, \text{m/s}) - (1.4 \, \text{m/s}^2) \cdot t
\]

Set \( v = 0 \) to solve for \( t \):
\[
0 = 4.2 - 1.4t
\]

Rearrange to find \( t \):
\[
1.4t = 4.2
\]
\[
t = \frac{4.2}{1.4} = 3.0 \, \text{s}
\]

Thus, the object changes direction at **3.0 seconds**.

The correct answer is:
**(B) 3.0 s**

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. How would the answer change if the acceleration term were positive instead of negative?
2. What does the slope of the velocity equation represent in terms of physics?
3. How can we determine if the object continues to accelerate after changing direction?
4. What would be the displacement of the object at the point where it changes direction?
5. How would you graph the velocity over time for this problem?

**Tip:** To analyze motion effectively, always check where velocity reaches zero to identify any change in direction.

At time t = 0 s, an object is moving to the right with a velocity v that can be modeled by the equation v = (4.2 m/s) - (1.4 m/s^2) * t. At what time, if any, does the object change its direction of motion? (A) 0.33 s, (B) 3.0 s, (C) 5.6 s, (D) At no time; the object never changes direction.

Solve a physics problem where an object's motion is given by v = (4.2 m/s) - (1.4 m/s^2) * t. Determine when the object changes direction by setting velocity to zero. This problem involves algebra and kinematics, suitable for Grades 10-12.

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