Math Problem Statement
An object moves in a one-dimensional motion starting at +4.5 m from the origin with a negative velocity of 2.1 m/s for 1.8 seconds. After that, it travels with a positive velocity of 6.3 m/s for 2 seconds. Immediately after that, it has a velocity equal to zero for 3.5 seconds. What is the final position of the object, expressed in meters to one decimal place?
Solution
We can break the problem down into three distinct stages of motion and calculate the displacement during each stage. We'll then add these displacements to the initial position of the object to find its final position.
Initial conditions:
- Initial position:
- Time intervals:
- Stage 1:
- Stage 2:
- Stage 3:
Stage 1: Negative velocity
- Velocity:
- Displacement during Stage 1:
Stage 2: Positive velocity
- Velocity:
- Displacement during Stage 2:
Stage 3: Velocity equals zero
- Velocity:
- Displacement during Stage 3:
Final position calculation:
The total displacement is the sum of the displacements from each stage:
The final position is the initial position plus the total displacement:
Final answer:
The final position of the object is 13.3 meters.
Would you like more details or have any questions?
Here are 5 questions related to this problem:
- How would the final position change if the initial velocity was positive instead of negative in Stage 1?
- What would be the total displacement if the object did not stop in Stage 3?
- How would air resistance affect the final position in this scenario?
- Could we calculate the average velocity of the object over the entire motion?
- How would the problem change if the object had a constant acceleration instead of constant velocity?
Tip: When dealing with motion problems, always break the motion into segments and calculate displacement for each separately.
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Math Problem Analysis
Mathematical Concepts
Kinematics
One-Dimensional Motion
Displacement
Velocity
Formulas
Displacement = velocity × time
Total displacement = sum of displacements
Final position = initial position + total displacement
Theorems
Equation of motion for constant velocity
Suitable Grade Level
Grades 9-12
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