Final answer:
The position of the particle at different times can be found using the equation x(t) = 4.0 - 2.0t. At t = 2.0 s, the position is 0.0 m. At t = 0 s, the position is 4.0 m. At t = -2.0 s, the position is 8.0 m. At t = 6.0 s, the position is -8.0 m.
Step-by-step explanation:
Given the equation for the position of the particle along the x-axis, x(t) = 4.0 - 2.0t, we can find the position of the particle at different times.
a) At t = 2.0 s, substitute t = 2.0 into the equation: x(2.0) = 4.0 - 2.0(2.0) = 4.0 - 4.0 = 0.0 m. Therefore, the position of the particle at t = 2.0 s is 0.0 m.
b) At t = 0 s, substitute t = 0 into the equation: x(0) = 4.0 - 2.0(0) = 4.0 m. Therefore, the position of the particle at t = 0 s is 4.0 m.
c) At t = -2.0 s, substitute t = -2.0 into the equation: x(-2.0) = 4.0 - 2.0(-2.0) = 4.0 + 4.0 = 8.0 m. Therefore, the position of the particle at t = -2.0 s is 8.0 m.
d) At t = 6.0 s, substitute t = 6.0 into the equation: x(6.0) = 4.0 - 2.0(6.0) = 4.0 - 12.0 = -8.0 m. Therefore, the position of the particle at t = 6.0 s is -8.0 m.