Question

match the unit with what it measures. all four must be correct to receive credit.
cm/y
in
d
m/y²
speed
time
displacement
acceleration

Explanation:

• For \( \text{cm/y} \): The unit \( \text{cm/y} \) (centimeters per year) is of the form \( \frac{\text{length}}{\text{time}} \). Speed is defined as the rate of change of displacement (a type of length - related quantity) with respect to time. So, \( \text{cm/y} \) measures speed.
• For \( \text{in} \): Inches (\( \text{in} \)) is a unit of length. Displacement is a vector quantity that measures the change in position (a length - like concept). So, \( \text{in} \) measures displacement.
• For \( \text{d} \): Days (\( \text{d} \)) is a unit of time.
• For \( \text{m/y}^2 \): The unit \( \text{m/y}^2 \) (meters per year squared) is of the form \( \frac{\text{length}}{\text{time}^2} \). Acceleration is defined as the rate of change of velocity (where velocity is \( \frac{\text{length}}{\text{time}} \)) with respect to time. So, \( \text{m/y}^2 \) measures acceleration.

Answer:

• \( \text{cm/y} \): speed
• \( \text{in} \): displacement
• \( \text{d} \): time
• \( \text{m/y}^2 \): acceleration