A hamster in a ball begins its journey 5 feet to the left of a refrigerator, travels 20 feet to the right of the refrigerator, and ends its journey directly in front of the refrigerator.

Question

If negative values are assigned to positions to the left of its starting position and positive values are assigned to positions to the right of its starting position, what is the displacement of the hamster?

Responses

5 feet
20 feet
0 feet
-5 feet

Answer 1

To determine the displacement of the hamster, we need to analyze its starting and ending positions relative to the refrigerator.

1. The hamster starts 5 feet to the left of the refrigerator. We can assign this position a value of -5 feet.
2. The hamster then travels 20 feet to the right. Since it starts at -5 feet and moves 20 feet to the right, we calculate its ending position as follows: \[ -5 \text{ feet} + 20 \text{ feet} = 15 \text{ feet} \]

So, after moving, the hamster ends up at +15 feet, which is 15 feet to the right of the refrigerator.

3. Finally, we need to find the displacement. Displacement is the difference between the final position and the initial position: \[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \] \[ \text{Displacement} = 15 \text{ feet} - (-5 \text{ feet}) = 15 + 5 = 20 \text{ feet} \]

Thus, the displacement of the hamster is 20 feet.

Answer 2

A cat wakes up in its bed and visits its food dish to the left of its bed.

Positions to the right of its bed are assigned a negative value and positions to the left of its bed are assigned a positive value.


Time (m) 1 2 3 4 5
Position (m) 0 2 4 -5 -10
Where did the cat begin and end its journey?

Responses

The cat began its journey in bed and ended its journey 10 meters to the right of its bed.

The cat began its journey at its food dish and ended its journey 10 meters to the left of its bed.

The cat began its journey in bed and ended its journey 5 meters to the left of its bed.

The cat began its journey at its food dish and ended its journey 10 meters to the right of its bed.

Answer 3

To analyze the cat's journey based on the provided position data, we first note the positions given for each time increment:

• At \( t = 1 \): Position = 0 m
• At \( t = 2 \): Position = 2 m
• At \( t = 3 \): Position = 4 m
• At \( t = 4 \): Position = -5 m
• At \( t = 5 \): Position = -10 m

Given that positions to the right of the bed are assigned a negative value and positions to the left are assigned a positive value, we can interpret the positions as follows:

• 0 m is the starting position (the cat's bed).
• 2 m and 4 m indicate positions to the left of the bed (positive values).
• -5 m and -10 m indicate positions to the right of the bed (negative values).

Therefore, the cat begins its journey at 0 m (its bed) and ends its journey at -10 m after moving to the right.

Now let's summarize the starting and ending positions:

• Starting position: In bed (0 m)
• Ending position: 10 meters to the right of its bed (-10 m)

Looking at the options provided:

• The cat began its journey in bed and ended its journey 10 meters to the right of its bed.

This is the correct interpretation based on the data.

Answer 4

Which statement correctly classifies distance and displacement?
Responses

Both distance and displacement are vector quantities.

Distance is a vector quantity, and displacement is a scalar quantity.

Distance is a scalar quantity, and displacement is a vector quantity.

Both distance and displacement are scalar quantities.

Answer 5

The correct statement that classifies distance and displacement is:

Distance is a scalar quantity, and displacement is a vector quantity.

Here's a brief explanation of why this is the case:

• Distance refers to the total length of the path traveled by an object, regardless of its direction. It is always a positive value and does not have a direction associated with it, making it a scalar quantity.

• Displacement refers to the change in position of an object and has both magnitude and direction (e.g., "10 meters to the east"). Because of this, displacement is classified as a vector quantity.

Therefore, the correct response is: Distance is a scalar quantity, and displacement is a vector quantity.

Answer 6

On a position vs. time graph, which feature would represent motion in the negative direction over time?
Responses

a vertical line segment

an upward-sloping line segment

a horizontal line segment

a downward-sloping line segment

Answer 7

On a position vs. time graph, motion in the negative direction over time is represented by:

a downward-sloping line segment.

Here's why:

• A downward-sloping line segment indicates that as time increases (moving to the right on the x-axis), the position is decreasing (moving down on the y-axis). This corresponds to an object moving in the negative direction.

• In contrast:

  • A vertical line segment would indicate that the position is not changing over time (the object is stationary).
  • An upward-sloping line segment indicates motion in the positive direction (position increasing).
  • A horizontal line segment again indicates that the position is constant (the object is stationary).

Thus, the correct answer is: a downward-sloping line segment.

Answer 8

Two construction workers are attempting to pull a slab of concrete off of the ground. Each of the workers are pulling up with a force of 225 N, while the slab of concrete applies a gravitational force of 400 N in the opposite direction, remaining stationary.

If the pulling forces applied to the slab of concrete are assigned a positive value, what is the net force of the scenario, and in which direction will the slab of concrete move?

Responses

-50 N; the slab will remain stationary

175 N; the slab will move upward

-175 N; the slab will remain stationary

50 N; the slab will move upward

Answer 9

To find the net force in the scenario, we can sum the forces acting on the slab of concrete.

1. Forces exerted by the workers:

   • Each worker pulls with a force of 225 N, and there are two workers, so the total upward force is: \[ \text{Total upward force} = 225 , \text{N} + 225 , \text{N} = 450 , \text{N} \]

2. Gravitational force on the slab:

   • The gravitational force acting downward is 400 N.

3. Calculating the net force: The net force (F_net) can be calculated using the formula: \[ F_{\text{net}} = \text{Total upward force} - \text{Downward force} \] Substituting the values we found: \[ F_{\text{net}} = 450 , \text{N} - 400 , \text{N} = 50 , \text{N} \]

Since the net force is 50 N in the upward direction, the slab will move upward.

Therefore, the correct response is: 50 N; the slab will move upward.

Answer 10

A stone with a mass of 10 kg sits on the ground. Gravity acts on the stone at a rate of 9.8 m/s2. What is the normal force acting on the stone, keeping it at rest?
Responses

98 N

9.8 N

10 N

1.02 N

Answer 11

To find the normal force acting on the stone while it is at rest on the ground, we can use the formula for weight, which is the force due to gravity acting on the object:

\[ \text{Weight} (W) = \text{mass} (m) \times \text{acceleration due to gravity} (g) \]

Given:

• Mass of the stone, \( m = 10 , \text{kg} \)
• Acceleration due to gravity, \( g = 9.8 , \text{m/s}^2 \)

Now, substituting the values into the formula:

\[ W = 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 98 , \text{N} \]

Since the stone is at rest on the ground, the normal force (N) acting on the stone will equal the weight of the stone but in the opposite direction. Therefore, the normal force is:

\[ N = 98 , \text{N} \]

So, the correct response is:

98 N.