- Introduction
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- Position and Displacement
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- Average velocity and speed
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- Instantaneous velocity and speed
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- Acceleration
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- Motion with constant acceleration
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- Free fall acceleration
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- Relative velocity
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- Solved Examples Part 1
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- Solved Examples Part 2
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- Solved Examples Part 3
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- Solved Examples Part 4
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- Solved Examples Part 5

- Position Distance and Displacement
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- Average velocity and speed
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- Velocity and acceleration
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- Uniformly accelerated motion
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- Relative Velocity
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- Kinematics Question 1
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- Kinematics Question 2

- Motion with constant acceleration or uniformly accelerated motion is that in which velocity changes at the same rate throughout motion.

- When the acceleration of the moving object is constant its average acceleration and instantaneous acceleration are equal. Thus from eq. 5 we have

- Let v
_{0}be the velocity at initial time t=0 and v be the velocity of object at some other instant of time say at t_{2}=t then above eq. 7 becomes

or , v=v_{0}+at (8)

- Graphically this relation is represented in figure 8 given below.

- Thus from the graph it can be seen clearly that velocity v at time t is equal to the velocity v
_{0}at time t=0 plus the change in velocity (at).

- In the same way average velocity can be written as

where x_{0}is the position of object at time t=0 and v_{avg}is the averag velocity between time t=0 to time t.The above equation then gives

x=x_{0}+v_{avg}t (9)

but for the interval t=0 to t the average velocity is

**v**= v_{avg}_{0}+ ½(at) (11)

putting this in eq. 9 we find

x = x_{0}+ v_{0}t + ½(at^{2})

or,

x - x_{0}= v_{0}t + ½(at^{2}) (12)

this is the position time relation for object having uniformly accelerated motion.

- From eq. 12 it is clear that an object at any time t has quadratic dependence on time, when it moves with constant acceleration along a straight line and x-t graph for such motion will be parabolic in natures shown below.

- Equation 8 and 12 are basic equations for constant acceleration and these two equations can be combined to get yet another relation for x , v and a eliminating t so, from 8

putting this value of t in equation 12 and solving it we finally get,

v^{2}= (v_{0})^{2}+ 2a ( x - x_{0}) (13)

- Thus from equation 13 we see that it is velocity displacement relation between velocities of object moving with constant acceleration at time t and t=0 and their corresponding positions at these intervals of time.

- This relation 13 is helpful when we do not know time t.

- Likewise we can also eliminate the acceleration between equation 8 and 12. Thus from equation 8

putting this value of a in equation 12 and solving it we finally get,

( x - x_{0}) = ½ ( v_{0}+ v ) t (14)

- Same way we can also eliminate v
_{0}using equation 8 and 12. Now from equation 8

v_{0}= v - at

putting this value of v_{0}in equation 12 and solving it we finally get,

( x - x_{0}) = vt + ½ ( at^{2}) (15)

thus equation 15 does not involve initial velocity v_{0} - Thus these basic equations 8 and 12 , and derived equations 13, 14, and 15 can be used to solve constant acceleration problems.

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