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Acceleration is nothing but rate of increase in velocity. If acceleration at the time is positive velocity will increase independent of acceleration in past.

Suppose you are moving at 5m/s at t=0. Acceleration is 5m/s2 initially. At t = 1 your velocity will be 10m/s. If acceleration became 3m/s2, then your velocity at t = 2 will be 13m/s. Thus your velocity still increased but comparatively lesser in amount. Now if acceleration became -8m/s2, velocity at t = 3 will be 5m/s, thus velocity decrease due to negative acceleration.

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