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How do velocity and acceleration differ?

Answer 1

Velocity and acceleration are two completely different quantities, but they are closely related to one another.

Velocity is the rate of change of position. Acceleration is the rate of change of velocity.

In other words, velocity will tell you how the position of an object is changing in time. Acceleration will tell you how the velocity of an object is changing in time.

In terms of calculus, we can formulate the following relation for a velocity function #v(t)#, and an acceleration function #a(t)#:

#=>a(t) = (dv(t))/(dt)#

or equivalently

#=>v(t) = int a(t) dt#

The units of velocity are #"m"/"s"# The units of acceleration are #"m"/"s"^2#

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Answer 2

Charles Aeschliman

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. Acceleration, also a vector quantity, describes the rate of change of an object's velocity with respect to time, indicating how quickly the velocity of an object is changing.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.