- 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

- Suppose a particle moves from point P to point Q in x-y plane as shown below in the figure

- Suppose
**v**_{1}is the velocity of the particle at point P and**v**_{2}is the velocity of particle at point Q

- Average acceleration is the change in velocity of particle from
**v**_{1}to**v**_{2}in time interval Δt as particle moves from point P to Q. Thus average acceleration is

Average accelaration is the vector quantity having direction same as that of Δ**v**.

- Again if point Q aproaches point P, then limiting value of average acceleration as time aproaches zero defines instantaneous acceleration or simply the acceleration of particle at that point. This, instantaneous acceleration is

- Figure below shows instantaneous acceleration a at point P.

- Instantaneous acceleration does not have same direction as that of velocity vector instead it must lie on the concave side of the curved surface.

- Thus velocity and acceleration vectors may have any angle between 0 to 180 degree between them.

The position of a object is given by

Where t is in second and coefficents have the proper units for r to be in centimeters

a) Find v(t) and a(t) of the object

b) Find the magnitude and direction of the velocity at t=3sec

It is given in the questions

Now

Therefore,

Now

Therefore,

So acceleration is 4 cm/s

Now velocity at 3 sec

So its magnitude is √(3

And direction will be tan

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