Here are three pairs of initial and final positions, respectively, along an x-axis. Which pair gives a
negative displacement: (a) -3 m, +5 m; (b)-3 m,-7 m; (c) 7 m, -3 m?

(b)-3 m,-7 m

Explanation:

Displacement is a vector quantity that connects the initial position of an object to its final position after a certain motion.

Mathematically, displacement can be written as:

where

is the final position

is the initial position

The direction of this vector is from the initial position to the final position.

In order to calculate the displacement of an object, therefore, it is necessary to correctly take into account the sign of each motion, which gives the direction of each motion.

Let's analyze the three cases:

(a) -3 m, +5 m;

In this case, the object moves 3 m in the negative direction first, and then 5 meters in the positive direction; so the net displacement is

d = -3 + 5 = +2 m

(b)-3 m,-7 m;

In this case, the object moves 3 m in the negative direction first, and then 3 meters in the negative direction; so the net displacement is

d = -3 - 7 = -10 m

(c) 7 m, -3 m?

In this case, the object moves 7 m in the positive direction first, and then 3 meters in the negative direction; so the net displacement is

d = +7 + (-3) = +4 m

So, the only situation in which we have a net negative displacement is situation b).

electric

explanation:

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