Distance And Displacement Quiz

Explanation
The player's total displacement from the batter's box is smaller than the total distance traveled because displacement refers to the straight-line distance between the starting and ending points, while distance traveled refers to the actual path taken. In this case, the player overran first base by 3.0 meters and then returned, resulting in a longer distance traveled. However, the displacement would only account for the straight-line distance between the batter's box and the final position, which would be smaller.

Explanation
To find the total displacement of the student, we can treat each block as a vector, where east is positive and west is negative on the x-axis, and north is positive and south is negative on the y-axis.
Walking 3 blocks east corresponds to a displacement of +3 units in the x-direction.
Walking 2 blocks north corresponds to a displacement of +2 units in the y-direction.
Walking 1 block west corresponds to a displacement of -1 unit in the x-direction.
Walking 2 blocks south corresponds to a displacement of -2 units in the y-direction.
Now, we can find the total displacement by adding these individual displacements together:
Total displacement in the x-direction = 3 (east) - 1 (west) = 3 - 1 = 2 units east. Total displacement in the y-direction = 2 (north) - 2 (south) = 2 - 2 = 0 units.
So, the total displacement of the student is 2 units east and 0 units north. This means the student ends up 2 blocks to the east of their starting point with no north-south displacement, resulting in a total displacement of 2 units east.

Explanation
The girl's total displacement from the history classroom to the art classroom is 20 meters south. This is because she initially walked 10 meters north, but then turned and walked 30 meters south. The northward and southward displacements cancel each other out, resulting in a net displacement of 20 meters south.

Explanation
The SI unit for displacement is meter. Displacement is a measure of the change in the position of an object and is usually measured in meters. It represents the shortest distance between the initial and final positions of an object, regardless of the path taken. Centimeters and kilometers are not the SI units for displacement, although they can be used for other measurements such as length or distance. Therefore, the correct answer is meter.

Explanation
Distance is a scalar quantity because it only has magnitude and no direction. Scalar quantities are described by a single value, such as distance, time, or temperature, and do not have any associated direction. In contrast, vector quantities have both magnitude and direction, such as velocity or displacement. Since distance only represents the magnitude of the displacement, it is considered a scalar quantity.

Explanation
The displacement of the car at the end of the 1.0-second interval is 20 meters east. Displacement refers to the change in position of an object, taking into account both the distance traveled and the direction. In this case, the car travels 20 meters in the east direction, so the displacement is 20 meters east. The units for displacement are distance units (meters) and the direction is indicated by the word "east".

Explanation
To find the magnitude of the resultant displacement, we can treat the student's movements as vectors and use vector addition. The displacement in the east direction is a vector of +1.0 kilometers, the displacement in the south direction is a vector of -1.0 kilometers, and the displacement in the west direction is a vector of -2.0 kilometers.
Now, let's add these vectors:
Resultant displacement in the east direction = +1.0 km Resultant displacement in the south direction = -1.0 km Resultant displacement in the west direction = -2.0 km
The resultant displacement vector, R, can be found by adding these vectors:
R = 1.0 km east - 1.0 km south - 2.0 km west
R = (1.0 km - 1.0 km - 2.0 km) = -2.0 km
The magnitude of the resultant displacement is the absolute value of this vector:
Magnitude of R = |-2.0 km| = 2.0 km
Therefore, the magnitude of the student's resultant displacement is closest to 2.0 kilometers.

Explanation
If an object travels a certain distance and returns to its starting point, its displacement will be zero. Displacement refers to the change in position of an object, and if the object returns to its initial position, there is no change in position or displacement. Therefore, the correct answer is zero.

Explanation
Since John covers 3 rounds on a circular track, he ends up back at the starting point. Displacement is the shortest distance between the initial and final positions. In this case, the displacement is zero because John's starting and ending points are the same.

Explanation
Michael travels 250 miles to the North and then backtracks to the South for 105 miles. Therefore, his net displacement is the difference between the two distances, which is 250 - 105 = 145 miles to the North.