Final answer:
Centripetal acceleration is given by the formula ac = v²/r. Using dimensional analysis, we can show that its units are m/s².
Step-by-step explanation:
Centripetal acceleration, denoted as ac, is given by the formula ac = v²/r. To show that centripetal acceleration has units of acceleration, we can use dimensional analysis. Let's break down the units of each component:
- v: velocity, which has units of meters per second (m/s).
- r: radius, which has units of meters (m).
Therefore, when we plug in these units into the formula, the units of centripetal acceleration are (m/s)²/m, which simplifies to m/s². So, the correct answer is (a) m/s².