- Introduction
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- Average velocity
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- Instantaneous velocity
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- Average and instantaneous acceleration
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- Motion with constant acceleration
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- Projectile Motion
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- Uniform circular motion
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- Motion in three dimensions

- We already know that instantaneous velocity is the velocity of the particle at any instant of time or at any point of its path.

- If we bring point Q more and more closer to point P and then calculate average velocity over such a short displacement and time interval then

where**v**is known as the instantaneous velocity of the particle.

- Thus, instantaneous velocity is the limiting value of average velocity as the time interval aproaches zero.

- As the point Q aproaches P, direction of vector Δ
**r**changes and aproaches to the direction of the tangent to the path at point P. So instantaneous vector at any point is tangent to the path at that point.

- Figure below shows the direction of instantaneous velocity at point P.

- Thus, direction of instantaneous velocity
**v**at any point is always tangent to the path of particle at that point.

- Like average velocity we can also express instantaneous velocity in component form

where v_{x}and v_{y}are x and y components of instantaneous velocity.

- Magnitude of instantaneous velocity is

|**v**|=√[(v_{x})^{2}+(v_{y})^{2}]

and angle θ which velocity vector makes with x-axis is

tanθ=v_{x}/v_{y}

- Expression for instantaneous velocity is

Thus, if expression for the co-ordinates x and y are known as function of time then we can use equations derived above to find x and y components of velocity.

Class 11 Maths page Class 11 Physics page

- Principles of Physics Extended (International Student Version) (WSE)
- university physics with modern physics by Hugh D. Young 13th edition
- NCERT Exemplar Problems: Solutions Physics Class 11
- H.C. Verma Concepts of Physics - Vol. 1
- CBSE All in One Physics Class 11 by Arihant
- NCERT Solutions: Physics Class 11th
- New Simplified Physics: A Reference Book for Class 11 (Set of 2 Parts)
- Pradeep's A Text Book of Physics with Value Based Questions - Class XI (Set of 2 Volumes)
- Oswaal CBSE Sample Question Papers For Class 11 Physics (For 2016 Exams)