Velocity is the integral of acceleration from rest

Steps:

• Identify that velocity starts at zero since the object begins from rest.
• Compute velocity at any time t as the area under the acceleration-time curve from 0 to t.
• The v-t graph's slope equals acceleration, so its shape mirrors the cumulative area of the a-t graph.
• Select the option where velocity increases proportionally to these areas over time.

Why A is correct:

• Option A matches the v-t graph where displacement under a-t (area) directly yields the velocity curve, per v = ∫a dt + v₀ (v₀=0).

Why the others are wrong:

• B incorrectly shows constant velocity, ignoring acceleration changes.
• C depicts decreasing velocity, contradicting positive acceleration areas.
• D has abrupt changes, not matching smooth integration of a-t.

Final answer: A