Question

Which of the following will have units of kg•m²/s²?

Select all that apply.
a. 1/2 mv²
b. maΔt
c. malΔt
d. mar
e. ma
f. mv

Answer 1

Main Answer:

a. 1/2 mv²: Kinetic energy formula; units derive from mass (kg) and velocity (m/s), yielding kg•m²/s².

c. malΔt: Force formula; mass (kg), acceleration (m/s²), and time (s) product, resulting in kg•m²/s².

f. mv: Linear momentum; mass (kg) multiplied by velocity (m/s) gives units of kg•m²/s².

Step-by-step explanation:

The expression that has units of
`kg•m²/s² is 1/2 mv²` and maΔt. The main formula for kinetic energy is 1/2 mv², where "m" represents mass (kg) and "v" represents velocity (m/s). The units of this expression are
`(kg • m²/s²),` indicating kinetic energy. Similarly, the expression maΔt corresponds to the work done, where "m" is mass (kg), "a" is acceleration (m/s²), and Δt is change in time (s). The units for this expression are also
`(kg • m²/s²),` representing the work done in the system.

On the other hand, expressions such as malΔt, mar, ma, and mv do not have units of
`kg•m²/s²`. malΔt represents force multiplied by distance and time, resulting in units of
`(kg • m/s² • s),` which simplifies to (kg • m²/s), representing momentum. The expressions mar and ma are both associated with force, having units of
`(kg • m/s²),` representing Newton's second law. Lastly, mv represents momentum, with units of
`(kg • m/s).`

In summary, 1/2 mv² and maΔt have units of kg•m²/s², aligning with the concepts of kinetic energy and work done. The other expressions do not match the required units.