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Linear Motion


Non-uniform Linear Acceleration








Consider a particle P moving in a straight line from a starting point O.


The displacement from O is x at time t .


The initial conditions are: t ≥ 0 when x=0.


If v is the velocity of P at time t, then :


v equals dx by dt


The acceleration 'a' of particle P is defined as:


definition of acceleration in terms of v and x


or alternately,


non uniform acceleration differential equations



Problems on this topic are solved by analysing the information given to form a differential equation. This is then integrated, usually between limits.



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Example #1


A particle moves in a straight line such that its acceleration 'a' at time 't' is given by:


problem #01a


If the initial speed of the particle is 5 ms-1, at what values of 't' is the particle stationary?



problem #01b



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Example #2


A particle moves from a point O in a straight line with initial velocity 4 ms-1.
if v is the velocity at any instant, the acceleration a of the particle is given by:


problem 2a


The particle passes through a point X with velocity 8 ms-1.


(i) how long does the particle take to reach point X?
(ii) what is the distance OX?(1 d.p.)




problem #2b




problem 2c





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