- Introduction
- |
- Average velocity
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- Instantaneous velocity
- |
- 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

- Motion in two dimension with constant acceleration we we know is the motion in which velocity changes at a constant rate i.e, acceleration remains constant throughout the motion

- We should set up the kinematic equation of motion for particle moving with constant acceleration in two dimensions.

- Equation's for position and velocity vector can be found generalizing the equation for position and velocity derived earliar while studying motion in one dimension

Thus velocity is given by equation

**v**=**v**+_{0}**a**t (8)

where

**v**is velocity vector

**v**is Intial velocity vector_{0}

**a**is Instantanous acceleration vector Similary position is given by the equation

**r**-**r**=_{0}**v**t+(1/2)_{0}**a**t^{2}(9)

where**r**is Intial position vector_{0}

i,e

**r**=x_{0}_{0}**i**+y_{0}**j**

and average velocity is given by the equation

**v**=(1/2)(_{av}**v**+**v**) (10)_{0}

- Since we have assumed particle to be moving in x-y plane,the x and y components of equation (8) and (9) are

v_{x}=v_{x0}+a_{x}t (11a)

x-x_{0}=v_{0x}t+(1/2)a_{x}t^{2}(11b)

and

v_{y}=v_{y0}+a_{y}t (12a)

y-y_{0}=v_{0y}t+(1/2)a_{y}t^{2}(12b)

- from above equation 11 and 12 ,we can see that for particle moving in (x-y) plane although plane of motion can be treated as two seperate and simultanous 1-D motion with constant acceleration

- Similar result also hold true for motion in a three dimension plane (x-y-z)

A object starts from origin at t = 0 with a velocity 5.0

(a) What is the y-coordinate of the particle at the instant its x-coordinate is 84 m ?

(b) What is the speed of the particle at this time ?

We know that position of the object is given by

Here

So

= (5t+1.5t

Now

Therefore,

x(t)=5t+1.5t

Given x=84

so 5t+1.5t

or t=6 sec

Then y= t

Now

At t=6sec

Speed =|

Relative velocity is defined as

where

Similiary relative velocity of A relative to B

we will need to add or subtracting components along x & y direction to get the relative velocity

Suppose

Relative velocity of B relative to A

=v

=

Relative velocity of B relative to A

=v

=

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