# How do velocity and acceleration differ?

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.

or equivalently

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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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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.

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.

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.

- An object's velocity is given by #v(t) = (t^2 -t +1 , t^3- 3t )#. What is the object's rate and direction of acceleration at #t=3 #?
- The position of an object moving along a line is given by #p(t) = sin(3t- pi /4) +2 #. What is the speed of the object at #t = (3pi) /4 #?
- What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = t^3-t+3# from #t in [2, 3]#?
- A car starts from rest and accelerates uniformly over a time of 10 seconds for a distance of 215 m. What is the acceleration of the car?
- An object's two dimensional velocity is given by #v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- t )#. What is the object's rate and direction of acceleration at #t=2 #?

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