Charlene33chidn
Answered

IDNLearn.com offers a seamless experience for finding and sharing knowledge. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.

7. A particle moves along the [tex]x[/tex] axis from [tex]x_i[/tex] to [tex]x_f[/tex]. Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

a. [tex]x_i = 4 \, \text{m}, \, x_f = 6 \, \text{m}[/tex]
b. [tex]x_i = -4 \, \text{m}, \, x_f = -8 \, \text{m}[/tex]
c. [tex]x_i = -4 \, \text{m}, \, x_f = 2 \, \text{m}[/tex]
d. [tex]x_i = 4 \, \text{m}, \, x_f = -2 \, \text{m}[/tex]

Sagot :

GinnyAnsweridn
To determine which displacement has the largest magnitude, let's go through the displacements for each given pair of initial and final coordinates step-by-step.

1. Option a: [tex]\(x_i = 4 \, \text{m}\)[/tex], [tex]\(x_f = 6 \, \text{m}\)[/tex]
- Displacement [tex]\( \Delta x_a = x_f - x_i = 6 \, \text{m} - 4 \, \text{m} = 2 \, \text{m} \)[/tex]
- Magnitude of displacement: [tex]\( |2 \, \text{m}| = 2 \, \text{m} \)[/tex]

2. Option b: [tex]\(x_i = -4 \, \text{m}\)[/tex], [tex]\(x_f = -8 \, \text{m}\)[/tex]
- Displacement [tex]\( \Delta x_b = x_f - x_i = -8 \, \text{m} - (-4 \, \text{m}) = -8 \, \text{m} + 4 \, \text{m} = -4 \, \text{m} \)[/tex]
- Magnitude of displacement: [tex]\( |-4 \, \text{m}| = 4 \, \text{m} \)[/tex]

3. Option c: [tex]\(x_i = -4 \, \text{m}\)[/tex], [tex]\(x_f = 2 \, \text{m}\)[/tex]
- Displacement [tex]\( \Delta x_c = x_f - x_i = 2 \, \text{m} - (-4 \, \text{m}) = 2 \, \text{m} + 4 \, \text{m} = 6 \, \text{m} \)[/tex]
- Magnitude of displacement: [tex]\( |6 \, \text{m}| = 6 \, \text{m} \)[/tex]

4. Option d: [tex]\(x_i = 4 \, \text{m}\)[/tex], [tex]\(x_f = -2 \, \text{m}\)[/tex]
- Displacement [tex]\( \Delta x_d = x_f - x_i = -2 \, \text{m} - 4 \, \text{m} = -2 \, \text{m} - 4 \, \text{m} = -6 \, \text{m} \)[/tex]
- Magnitude of displacement: [tex]\( |-6 \, \text{m}| = 6 \, \text{m} \)[/tex]

Now, let's compare the magnitudes of these displacements:

- Magnitude of displacement for option a: [tex]\( 2 \, \text{m} \)[/tex]
- Magnitude of displacement for option b: [tex]\( 4 \, \text{m} \)[/tex]
- Magnitude of displacement for option c: [tex]\( 6 \, \text{m} \)[/tex]
- Magnitude of displacement for option d: [tex]\( 6 \, \text{m} \)[/tex]

The largest magnitude of displacement is [tex]\( 6 \, \text{m} \)[/tex], which occurs in both option c and option d. Therefore, the displacements with the largest magnitude are given in:

Option c: [tex]\( x_i = -4 \, \text{m} \)[/tex], [tex]\( x_f = 2 \, \text{m} \)[/tex] and Option d: [tex]\( x_i = 4 \, \text{m} \)[/tex], [tex]\( x_f = -2 \, \text{m} \)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.