Question

Are the units of the formula ma =mv² /2 dimensionally consistent? Select the single best answer

a)no-ma has units of kg.m/s² and 1/2mv² has units of kg.m²/s²
b)no-ma has units of kg.m/s and 1/2mv² has units of kg m²/s²
c)yes-both ma and 1/2mv² have units of kg.m²/s²
d)no -ma has units of kg.m²/s² and 1/2m² has units of kg.m/s²
e)yes-both ma and 1/2mv² have units of kg*m/s²
f)yes-the units of m cancel on both sides.
g)yes-both ma and 1/2mv² have units of kg.m/s

Answer 1

The units for ma and mv²/2 are both dimensionally consistent and the same; they are kg·m/s², which correspond to the units of force (newtons) and energy (joules) respectively.

Step-by-step explanation:

The question is asking whether the units for the formulas ma and mv²/2 are dimensionally consistent. To determine this we simply check each formula's units. For ma, where m is mass in kilograms (kg) and a is acceleration in meters per second squared (m/s²), the units are kg·m/s², which represent force (in newtons, N). For the kinetic energy K = 0.5mv², where v is velocity in m/s, the units are kg·m²/s², which simplify to kg·m/s² since the 1/2 is dimensionless. This is also the unit for energy (joules, J). Thus, the correct answer is e)yes-both ma and 1/2mv² have units of kg·m/s².