Scalars, Vectors & Graphs

Which of the following is a scalar quantity?

• Velocity

• Distance

• Displacement

• Force

Answer explanation

Distance is a scalar quantity as it only has magnitude and no direction. In contrast, velocity, displacement, and force are vector quantities, which have both magnitude and direction.

What is the definition of a vector quantity?

• A quantity that has only magnitude

• A quantity that has both magnitude and direction

• A quantity that has only direction

• A quantity that is always positive

Answer explanation

A vector quantity is defined as one that possesses both magnitude and direction, distinguishing it from scalar quantities, which have only magnitude. Therefore, the correct answer is that a vector quantity has both magnitude and direction.

Which of the following best describes displacement?

• The total length of the path traveled

• The change in position from the starting point to the ending point

• The speed at which an object moves

• The total time taken to travel

Answer explanation

Displacement refers to the change in position from the starting point to the ending point, making it a vector quantity. It differs from distance, which measures the total length of the path traveled.

What does the slope of a position vs. time graph represent?

• Acceleration

• Distance

• Speed

• Displacement

Answer explanation

The slope of a position vs. time graph indicates how quickly an object changes its position, which is defined as speed. Therefore, the correct answer is speed, not acceleration, distance, or displacement.

Which of the following is NOT a vector quantity?

• Displacement

• Weight

• Distance

• Velocity

Answer explanation

Distance is a scalar quantity, representing only magnitude, while displacement, weight, and velocity are vector quantities that include both magnitude and direction.

If an object moves 10 meters east and then 10 meters west, what is its displacement?

• 0 meters

• 10 meters

• 20 meters

• 5 meters

Answer explanation

Displacement is the shortest distance from the initial to the final position. The object moves 10 meters east and then 10 meters west, returning to the starting point, resulting in a displacement of 0 meters.

Which of the following statements is true about distance and displacement?

• Distance can be negative, but displacement cannot.

• Displacement is always greater than distance.

• Distance is always equal to or greater than displacement.

• Distance and displacement are always the same.

Answer explanation

Distance is the total path traveled, while displacement is the shortest straight-line distance from the starting point to the endpoint. Therefore, distance is always equal to or greater than displacement.

What is the formula for calculating the slope of a straight line on a position vs. time graph?

Answer explanation

The slope of a straight line on a position vs. time graph is calculated using the formula \(\frac{\Delta y}{\Delta x}\), where \(\Delta y\) represents the change in position and \(\Delta x\) represents the change in time.

Tags

NGSS.MS-PS3-1

Which of the following is an example of a scalar quantity?

• 5 meters north

• 10 m/s east

• 20 kg

• 15 N downward

Answer explanation

A scalar quantity has only magnitude, while a vector has both magnitude and direction. '20 kg' is a scalar as it only indicates mass. The other options include directional components, making them vector quantities.

A position vs. time graph shows a straight line with a positive slope. What does this indicate about the motion of the object?

• The object is at rest.

• The object is moving at a constant velocity.

• The object is accelerating.

• The object is moving backward.

Answer explanation

A straight line with a positive slope on a position vs. time graph indicates that the object is moving away from the starting point at a constant rate, meaning it is moving at a constant velocity.

Tags

NGSS.MS-PS3-1