A particle moves along the x-axis from an initial position xi to a final position xf. Of the following values of xi and xf, which results in a negative displacement? (a) xi = 6 m, xf = 4 m (b) xi = ?4 m, xf = ?2 m (c) xi = ?4 m, xf = 2 m (d) xi = 4 m, xf = 6 m (e) xi = ?4 m, xf = 4 m
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A particle moves along the x-axis from an initial position xi to a final position xf. Of the following values of xi and xf, which results in a negative displacement? (a) xi = 6 m, xf = 4 m (b) xi = -4 m, xf = -2 m (c) xi = -4 m, xf = 2 m (d) xi = 4 m, xf = 6 m (e) xi = -4 m, xf = 4 m
Displacement is xf-xi. If xf-xi > 0, the displacement is positive.
If xf-xi < 0, it is negative.
So if you calculate xf-xi and check the sign, you will get the answer quite soon.
To determine the displacement, we subtract the initial position from the final position.
(a) xi = 6 m, xf = 4 m:
Displacement = xf - xi = 4 m - 6 m = -2 m (negative displacement)
(b) xi = -4 m, xf = -2 m:
Displacement = xf - xi = -2 m - (-4 m) = 2 m (positive displacement)
(c) xi = -4 m, xf = 2 m:
Displacement = xf - xi = 2 m - (-4 m) = 6 m (positive displacement)
(d) xi = 4 m, xf = 6 m:
Displacement = xf - xi = 6 m - 4 m = 2 m (positive displacement)
(e) xi = -4 m, xf = 4 m:
Displacement = xf - xi = 4 m - (-4 m) = 8 m (positive displacement)
Therefore, the value of xi and xf that results in a negative displacement is (a) xi = 6 m, xf = 4 m.
To determine which combination of initial position (xi) and final position (xf) results in a negative displacement, we need to compare the values of xi and xf.
Displacement is the change in position of an object, which can be calculated by subtracting the initial position from the final position:
Displacement (Δx) = xf - xi
If the value of displacement is negative, it means the object has moved to the left or in the negative direction along the x-axis.
Let's calculate the displacements for each combination of xi and xf:
(a) xi = 6 m, xf = 4 m
Δx = 4 m - 6 m = -2 m (Negative displacement)
(b) xi = -4 m, xf = -2 m
Δx = -2 m - (-4 m) = 2 m (Positive displacement)
(c) xi = -4 m, xf = 2 m
Δx = 2 m - (-4 m) = 6 m (Positive displacement)
(d) xi = 4 m, xf = 6 m
Δx = 6 m - 4 m = 2 m (Positive displacement)
(e) xi = -4 m, xf = 4 m
Δx = 4 m - (-4 m) = 8 m (Positive displacement)
So, the only combination that results in a negative displacement is (a) xi = 6 m, xf = 4 m.