Question

Which of the following does not indicate velocity?

A. 14 feet per second per second
C. 80 miles per hour towards New York
B. 40 miles per hour towards town
D. 28 miles per second towards Ohio

Answer 1

A. 14 feet per second per second does not indicate velocity.

Step-by-step explanation:

Velocity has formula of displacement over time. Displacement can have unit such as mile, meter, kilometer, etc while time can have unit such as second, hour, minute, etc.

With division rule of term, we would have unit of measurement over unit of time, thus velocity only have one-degree term (no power term).

Unlike acceleration, acceleration has square term in time unit because acceleration is change in velocity over time. Velocity has unit of measurement over unit of time, with these units dividing another unit of time, we have:

`\displaystyle{ \frac{ \text{measurement}}{ \text{time}} / \text{time} = \frac{ \text{measurement}}{ \text{time}} * \frac{1} {\text{time} } \to \frac{ \text{measurement}}{ \text{time}^(2) }}`

Hence, acceleration would have time² unit while velocity only has time¹ unit.

And as seen in the choices, only unit that appears as time² is A choice as feet per second per second means (feet/second)/second = feet/sec² and this is acceleration, not velocity.