Position, Distance, And Displacement Simulation Quiz

1.

Brian is at school and wants to walk home. How far and in what direction should he travel? A negative value means the negative x-direction, and a positive value means the positive x-direction.

Explanation
Brian should travel a distance of 14 meters in the negative x-direction to reach home. The negative value indicates that he needs to move in the opposite direction of the positive x-axis. The additional information provided in meters confirms the unit of measurement for the distance traveled.

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2.

How far is he from school? (what is his distance from school?)

Explanation
The answer "14, 14m" suggests that the person is both 14 units and 14 meters away from the school. This could indicate that the person is measuring their distance from the school in two different units of measurement, or that they are referring to two different locations or points of reference. Without further context, it is difficult to determine the exact meaning of the answer.

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3.

Input the displacement vector from the school to his friend's house.

Explanation
The given answer, 0x + 7y,0x+7y, represents the displacement vector from the school to his friend's house. The vector has a magnitude of 7 units in the y-direction and no displacement in the x-direction, as indicated by the 0x term. This means that the friend's house is located 7 units directly above the school.

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4.

Enter the numbers for the displacement vector from his friend's house to his home.

Explanation
The given answer is the correct representation of the displacement vector from his friend's house to his home. The vector is described in terms of its x and y components, with -14x representing the displacement in the x-direction and -7y representing the displacement in the y-direction. The negative signs indicate that the displacement is in the opposite direction of the positive x and y axes.

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5.

Now why are these numbers negative? Choose the best reason why:

A.

He was walking backwards.
B.

His endpoint was in the negative x-direction AND in the negative y-direction, compared to his starting point.
C.

It means he was feeling bad during the walk home.

Correct Answer
B. His endpoint was in the negative x-direction AND in the negative y-direction, compared to his starting point.

Explanation
The reason why the numbers are negative is because the endpoint was in the negative x-direction AND in the negative y-direction, compared to the starting point. This indicates that the person moved towards the left (negative x-direction) and downwards (negative y-direction) from their starting point.

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6.

Displacement vector for house to school:

Correct Answer
14x + 0y
14x+0y

Explanation
The given displacement vector represents the distance and direction from the house to the school. The vector is represented in terms of x and y coordinates, where x represents the horizontal distance and y represents the vertical distance. The vector is written as 14x + 0y, which means that the horizontal displacement is 14 units in the x direction and there is no vertical displacement (0 units in the y direction). The repetition of the vector (14x + 0y, 14x + 0y) suggests that the displacement vector remains the same throughout the journey from the house to the school.

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7.

Displacement vector for school to friend's house:

Correct Answer
0x + 7y
0x+7y

Explanation
The given expression represents the displacement vector from school to a friend's house. The "0x" component indicates that there is no displacement in the x-direction, while the "7y" component indicates a displacement of 7 units in the y-direction. Therefore, the overall displacement vector is "0x + 7y".

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8.

Displacement vector for park to friend's house

Correct Answer
11x + -3y
11x+-3y

Explanation
The displacement vector for going from the park to the friend's house is represented by the expression 11x + -3y or 11x + -3y. The "x" and "y" variables represent the horizontal and vertical components of the displacement respectively. The positive coefficient of 11x indicates a movement towards the right or positive x-direction, while the negative coefficient of -3y indicates a movement downwards or negative y-direction. Therefore, the displacement vector is a combination of moving right and downwards.

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9.

Displacement vector for house to park

Correct Answer
3x + 10y
3x+10y

Explanation
The given expression, 3x + 10y, represents the displacement vector from the house to the park. The "3x" term indicates the displacement in the x-direction, while the "10y" term represents the displacement in the y-direction. Therefore, the vector 3x + 10y gives the combined displacement in both the x and y directions. The repetition of the expression, 3x+10y, is likely a typo or error in the question.

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10.

Brian's total displacement vector starts from his initial location (his house 2,1) and ends at his final location (his friends house 16,8). In other words, it starts at the base of the first vector and ends at the tail of the last vector. What are the values of this total displacement vector?

Correct Answer
14x + 7y
14x+7y

Explanation
The total displacement vector can be calculated by subtracting the initial position vector from the final position vector. In this case, the initial position vector is (2,1) and the final position vector is (16,8). Subtracting the initial position vector from the final position vector gives us (16-2, 8-1) which simplifies to (14,7). Therefore, the values of the total displacement vector are 14x + 7y.

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11.

For Brian's trip from his house to the fountain, why is the ŷ vector larger than the x̂ vector?

A.

He walked further in the y direction than the x.
B.

The y direction was "up" so its a large number.
C.

He walked faster in the y direction than he did the x direction.

Correct Answer
A. He walked further in the y direction than the x.

Explanation
The ŷ vector represents the distance traveled in the y direction, while the x̂ vector represents the distance traveled in the x direction. Since it is stated that Brian walked further in the y direction than the x, it implies that the magnitude of the ŷ vector is larger than the magnitude of the x̂ vector. Therefore, the ŷ vector is larger than the x̂ vector.

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12.

For Brian's trip from the fountain to his friend's house, why is the ŷ vector negative?

A.

Going to school is negative.
B.

They walked in the negative y direction.
C.

They walked slower in the y direction.

Correct Answer
B. They walked in the negative y direction.

Explanation
The ŷ vector represents the direction in the y-axis. If Brian and his friend walked in the negative y direction, it means they moved downwards or in the opposite direction of the positive y-axis. This is why the ŷ vector is negative in this scenario.

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13.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the x segment of the total displacement vector. What is the displacement x component of vector for A to B

Correct Answer
3x
3x
3

Explanation
The displacement x component of the vector from point A to point B is 3x.

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14.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the x segment of the total displacement vector. What is the x componenet displacement vector for B to C

Correct Answer
11x
11x
11

Explanation
The x component of the displacement vector from B to C is 11x.

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15.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the x segment of the total displacement vector. What is x component of the total (A to C) displacement vector

Correct Answer
14x
14

Explanation
The x component of the total displacement vector from A to C is 14x. This means that when Brian walks from his house to the park and then to his friend's house, the displacement in the x direction is 14x. The 14 represents the magnitude of the displacement, while the x indicates that the direction of the displacement is in the x direction.

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16.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the y segment of the total displacement vector. What is the displacement y component of vector for A to B

Correct Answer
10y
10

Explanation
The displacement y component of the vector from A to B is 10y. This means that the y-coordinate of point B is 10y units higher than the y-coordinate of point A. The 10 in the answer represents the magnitude of the displacement in the y-direction, while the y indicates that the displacement is dependent on the value of y.

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17.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the y segment of the total displacement vector. What is the displacement y component of vector for B to C

Correct Answer
-3y
-3

Explanation
The displacement y component of the vector from B to C is -3y. This means that Brian moves 3 units downward in the y direction from point B to point C. The negative sign indicates the direction of the displacement, which is downward. The "y" in -3y represents the magnitude of the displacement in the y direction.

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18.

Brian walks from his house (located at A) to the park (located at B), and then to his friend's house (located at C). Let's find how to calculate the y segment of the total displacement vector. What is the displacement y component of vector for A to C

Correct Answer
7y
7

Explanation
The displacement y component of the vector for A to C is given by "7y, 7". This means that the displacement in the y direction is equal to 7y units, while the displacement in the x direction is equal to 7 units.

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