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What is instantaneous velocity

What is instantaneous velocity

Grade:12

7 Answers

shiddhant bhattacharya
25 Points
7 years ago

Instantaneous velocity

Now the idea of average velocity is something that is fairly straightforward, but the idea of instantaneous velocity is a little trickier. It really requires calculus to fully appreciate, but hopefully you already know what a derivative is, so this shouldn''t be too hard.

Suppose the velocity of the car is varying, because for example, you''re in a traffic jam. You look at the speedometer and it''s varying a lot, all the way from zero to 60 mph. What is the instantaneous velocity? It is, more or less, what you read on the speedometer. I''m assuming you''ve got a good speedometer that isn''t too sluggish and can change its reading quite quickly. Your speedometer is measuring the the average velocity but one measured over quite a short time, to ensure that you''re getting an up to date reading of your velocity.

So if you measure the displacement of the car tex2html_wrap_inline1374 over a time tex2html_wrap_inline1376 , you can use that to determine the average velocity of the car. What we want is to take the limit as tex2html_wrap_inline1376 goes to zero. More formally, the instantaneous velocity v is defined as

equation121

 

Most of the time we''ll be working with instantaneous velocity, so we''ll just drop the instantaneous, and call the above v the velocity.

To justify that such a limit exists is something that you''ve hopefully had to grapple with already. For physics problems, this limit does indeed exist and gives the derivative:

  equation125

Prakhar Srivastava
18 Points
7 years ago

Dear Vineet Bramhankar

Suppose the velocity of the car is varying, because for example, you''re in a traffic jam. You look at the speedometer and it''s varying a lot, all the way from zero to 60 mph. What is the instantaneous velocity? It is, more or less, what you read on the speedometer. I''m assuming you''ve got a good speedometer that isn''t too sluggish and can change its reading quite quickly. Your speedometer is measuring the the average velocity but one measured over quite a short time, to ensure that you''re getting an up to date reading of your velocity.

So if you measure the displacement of the car tex2html_wrap_inline1374 over a time tex2html_wrap_inline1376 , you can use that to determine the average velocity of the car. What we want is to take the limit as tex2html_wrap_inline1376 goes to zero. More formally, the instantaneous velocity v is defined as

        

Please ApproveSmile


 

 

Akash Kumar Dutta
98 Points
7 years ago

velocity at that instant...given by dx/dt

Sameer Gupta
14 Points
7 years ago

A particle can have different velocities at different instant.Instantaneous velocity of a particle is simply the velocity of the particle at any of such instant.To understand,take example of speedometer of a car or a bike.It shows instanteneous velocity of that vechile.Generally in questions,instantaneous velocity is asked to find with the equation of motion in 2-d or 3-d dimension given.

Snehashis Parashar
36 Points
7 years ago

The velocity of a particle at a given instant of time is called instantaneous valocity. It is defined as the rate of change of position r (where r represents vector r ) w.r.t. time t.

v= dr/dt= (dx/dt)i + (dy/dt)j + (dz/dt)k

FITJEE
43 Points
7 years ago

So if you measure the displacement of the car tex2html_wrap_inline1374 over a time tex2html_wrap_inline1376 , you can use that to determine the average velocity of the car. What we want is to take the limit astex2html_wrap_inline1376 goes to zero. More formally, the instantaneous velocity v is defined as

equation121

 

Most of the time we''ll be working with instantaneous velocity, so we''ll just drop the instantaneous, and call the above v the velocity.

To justify that such a limit exists is something that you''ve hopefully had to grapple with already. For physics problems, this limit does indeed exist and gives the derivative:

  equation125

 

OR YOU CAN SIMPLY SAY THAT INSTNTANOUS VELOCITY IS THE VELOCITY OF A PARTICLE AT A PARTICULAR  INSTANT..


vivek kumar
57 Points
7 years ago

dx/dt

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