The time rate of increase in velocity is called

1. Analyze the question The question asks for the quantity defined as the "time rate of increase in velocity". "Time rate" means "change per unit time", so we are looking for the quantity that tells us how quickly velocity changes.

2. Explain the concept Acceleration is the rate of change of velocity with time:

a = (v − u) / t

where

• u = initial velocity
• v = final velocity
• t = time taken

Its SI unit is metres per second squared (m/s²).

3. Check each option

• A. Force is a push or pull. It is measured in newtons (N) and given by F = ma. It is not a rate of change of velocity.
• B. Momentum is mass × velocity (p = mv), measured in kg m/s. The rate of change of momentum gives force, not the rate of change of velocity.
• C. Acceleration is the change in velocity per unit time, which matches the definition exactly.
• D. Speed is the rate of change of distance with time (distance/time), not of velocity.

4. Answer The time rate of increase in velocity is acceleration, which is option C.

5. Exam tip Remember the "rate of change" chain:

• Rate of change of distance → speed
• Rate of change of displacement → velocity
• Rate of change of velocity → acceleration
• Rate of change of momentum → force

When a question says "rate of", ask yourself "rate of what?", and the answer is usually the next quantity in this chain.