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How to find Instantaneous Velocity in Calculus – Simple Steps to Solve It

Getting stuck while doing Calculus is probably one of the most frustrating feelings ever. It is already a tough subject, and if you are like me, you probably dread working on it. But, there’s no way out because it is important. All of us have to go through the struggle and work hard towards achieving a desirable result. 

But, this doesn’t mean that the path should be difficult. If there are ways you can make things easier for yourself, you should try them! We are here to help you with a few problems. In this guide, we will speak about instantaneous velocity and how you can find it. 

What is velocity?

Velocity is nothing but the measurement of how quickly a given object can move from point A to point B. It can also change with time depending on whether it is accelerating, decelerating, or moving at a constant speed. 

What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a given time. It describes the limit of velocity instead of speaking of the object’s change in position. Here are some points that you should remember:

  • Instantaneous velocity is a vector. This means that it has a direction and a value. 
  • The units used in this case are meters per second or m/s.

How to find Instantaneous Velocity in Calculus?

The formula to calculate instantaneous velocity

Instantaneous velocity = limit as a change in time goes to zero (change in position/change in time)

If you remember this formula, you will be able to solve your instantaneous velocity-related questions with the utmost ease. 

Solving instantaneous velocity from a graph 

The graph in question is a displacement versus time graph. You will need to learn the graph’s equation to solve Calculus instantaneous velocity. The equation is d = f(t). Start with t and find its derivative. Then, you can determine the equation for velocity through this because it will be a function of time. 

Now, all you have to do is substitute the values, and you will get the answer. That’s the instantaneous velocity at a given time. 

It may seem extremely daunting, but instantaneous velocity is not difficult to grasp. Once you solve a couple of problems on your own, you will understand better. Try new problems and make it a habit to practice every day. After all, calculus is only fun when you befriend it. 

If you have any doubts or questions, please feel free to Comment. We are always happy to help! ☺

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