Question

which best defines the relationship between speed and velocity?
speed is velocity with displacement.
velocity is speed with displacement.
speed is based on a specific direction
velocity is based on distance.

Explanation:

To determine the relationship between speed and velocity, we recall their definitions:

• Speed is a scalar quantity that measures the rate of change of distance (how fast an object moves, regardless of direction), calculated as \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).
• Velocity is a vector quantity that measures the rate of change of displacement (includes both speed and direction), calculated as \( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \).

Now, analyze each option:

• "Speed is velocity with displacement": Incorrect. Speed does not involve displacement (displacement is a vector, speed is scalar).
• "Velocity is speed with displacement": Correct. Velocity combines the magnitude of speed with the direction (implied by displacement, as displacement is a vector with direction).
• "Speed is based on a specific direction": Incorrect. Speed has no direction (it is scalar), while velocity does.
• "Velocity is based on distance": Incorrect. Velocity is based on displacement (a vector), while speed is based on distance (a scalar).

Answer:

B. Velocity is speed with displacement.