Math Problem Statement

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.

Solution

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

Given: v=(4.2m/s)(1.4m/s2)tv = (4.2 \, \text{m/s}) - (1.4 \, \text{m/s}^2) \cdot t

Set v=0v = 0 to solve for tt: 0=4.21.4t0 = 4.2 - 1.4t

Rearrange to find tt: 1.4t=4.21.4t = 4.2 t=4.21.4=3.0st = \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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Kinematics
Linear Equations

Formulas

v = v0 + at

Theorems

Concept of velocity reaching zero for change in direction

Suitable Grade Level

Grades 10-12