How is acceleration defined?

• A. distance/time
• B. change in velocity/change in time
• C. mass x acceleration
• D. acceleration/change in time

Answer: (B)

Acceleration is the rate at which velocity changes, defined as the change in velocity divided by the time over which that change occurs. In other words, a = Δv/Δt, with instantaneous acceleration given by the derivative dv/dt. This means it tells you how quickly an object's motion is speeding up or slowing down. For example, if velocity goes from 0 to 20 m/s in 4 seconds, acceleration is 20/4 = 5 m/s^2.

Distance divided by time gives speed, not acceleration, so that option isn’t the definition. Mass times acceleration equals force, not acceleration itself, so that alternative isn’t correct either. Dividing acceleration by time would yield a different quantity with units of m/s^3 and is not how we define acceleration (though it relates to how acceleration itself changes over time).