,
Linear Motion : Non-uniform Acceleration
 

[ theory ][ example#1][ example#2 ]

 

 

 

 

Theory

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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linear motion
acceleration
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connected particles
KE & PE changes
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elastic strings
conservation momtm.
coefft. restitution
 
 

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TOPIC NOTES(.pdf)

 
uniform acceleration
non-uniform accln.
simple harmonic motion
projectiles
circular motion
relative motion
Newton's Laws
connected particles
work & energy
power & efficiency
more circular motion
elastic strings
impulse
conservation momtm
coeff. restitution
part. forces in equilib.
friction
rigid bodies
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